It is “very likely” that the UK voted for Brexit because of illegal overspending by the Vote Leave campaign, according to an Oxford professor’s evidence to the High Court.

An exhaustive analysis of the campaign’s digital strategy concludes it reached “tens of millions of people” in its last crucial days, after its spending limit had been breached – enough to change the outcome.

The evidence will be put to the High Court on Friday, in a landmark case that is poised to rule within weeks whether the referendum result should be declared void because the law was broken.

Professor Philip Howard, director of the Oxford Internet Institute, at the university, said: “My professional opinion is that it is very likely that the excessive spending by Vote Leave altered the result of the referendum.

“A swing of just 634,751 people would have been enough to secure victory for Remain.

“Given the scale of the online advertising achieved with the excess spending, combined with conservative estimates on voter modelling, I estimate that Vote Leave converted the voting intentions of over 800,000 voters in the final days of the campaign as a result of the overspend.”

The conclusion came as Theresa May scrambled to find a concession she could give to rebel Tories to persuade them to back her deal, as she appeared to be veering towards a heavy defeat in next Tuesday’s landmark vote.

Professor Howard’s report is based on separate research which found that 20-30 per cent of people decided how to vote within a week of polling day, with half of these doing so on election day itself.

If, as he has concluded, Vote Leave’s Facebook adverts reached tens of millions of people after they should have stopped, they influenced huge numbers of voting decisions.

Now the campaigners will ask the High Court for permission to use the report as evidence, when a potentially explosive legal challenge gets underway on Friday.

The Independent revealed last month that lawyers expect the judges will fast-track the case to a full hearing because of the prime minister’s refusal to act on the growing evidence of illegality in the 2016 referendum campaign.

A historic moment: thousands march to demand Final Say on Brexit Show all 65 1 /65 A historic moment: thousands march to demand Final Say on Brexit A historic moment: thousands march to demand Final Say on Brexit An estimated 700,000 people marched through London to demand a final say on the withdrawal agreement Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Red smoke from a canister hangs in the air as around 100,000 demonstrators march through London during a People's Vote anti-brexit demonstration savings banners and placards Anti-Brexit People's Vote March for the Future in London Rex A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Mayor of London Sadiq Khan takes part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum. PA A historic moment: thousands march to demand Final Say on Brexit Final Say campaigners take part in the peoples vote march for the future in London 20/10/2018 Protesters wearing final Say shirts and holding placards Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit MP Chuka Umunna (left) and MP Vince Cable (right) as MP Anna Soubry (centre) addresses Anti-Brexit campaigners at a rally after the People's Vote March for the Future in London, a march and rally in support of a second EU referendum. PA A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit A People’s Vote march attendee calls for a Final Say Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Demonstrators with banners 'We're with EU' during the People's Vote March for the Future in London, Britain, 20 October 2018. Reports state that the 'March for the Future' is to be led by a column of young people and call for a Peopleâ€™s Vote on the Brexit deal. After marching through central London, there will be a rally on stage in Parliament Square, including speeches from Mayor of London Sadiq Khan. EPA A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Protesters at London’s march for the future in October The Independent A historic moment: thousands march to demand Final Say on Brexit Editor of The Independent Christian Broughton speaks to demonstrators in Parliament Sqaure after they take part in a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit A poster at the March for the Future in October The Independent A historic moment: thousands march to demand Final Say on Brexit Anti-Brexit campaigners take part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum. PA A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say campaigners take part in the peoples vote march for the future in London 20/10/2018 Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Anti-Brexit campaigners take part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum. PA A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Demonstrators hold placards as they take part in a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Final Say campaigners take part in the peoples vote march for the future in London 20/10/2018 campaigner wrapped in EU flag Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say campaigners take part in the peoples vote march for the future in London 20/10/2018 Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Demonstrators pass Trafalgar Square as they take part in a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit Demonstrators wave Union and European flags and hold up placards as they pass Trafalgar Square, taking part in a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit Demonstrators hold placards as they take part in a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit A demonstrator holds a message during a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit Anti-Brexit campaigners take part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum. PA A historic moment: thousands march to demand Final Say on Brexit Demonstrators take part in the 'People's Vote March for the Future,' in central London, Britain, 20 October 2018. Reports state that the 'March for the Future' is to be led by a column of young people and call for a Peopleâ€™s Vote on the Brexit deal. After marching through central London, there will be a rally on stage in Parliament Square, including speeches from Mayor of London Sadiq Khan EPA A historic moment: thousands march to demand Final Say on Brexit A protester brandishes an Independent t-shirt during the Brexit March Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Anti-Brexit campaigners take part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum PA A historic moment: thousands march to demand Final Say on Brexit Tens of thousands of people take part in People's Vote March for the Future in central London. The march organised by the People's Vote campaign is led by young people calling for a People's Vote on the Brexit deal Rex A historic moment: thousands march to demand Final Say on Brexit Anti-Brexit campaigners take part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum PA

The case is expected to move to a full hearing and a ruling within weeks of opening, with the clock ticking on the UK’s departure from the EU next March.

The government is set to deploy Sir James Eadie QC – the barrister who led the unsuccessful battle for the government to trigger Article 50 without parliament’s consent – in a sign of the case’s importance.

Professor Howard based his study on material disclosed by Facebook to the Commons committee which investigated Vote Leave’s overspending, as well “accounts written by campaign insiders”.

It points out that the Remain campaign was forced to stop its digital advertising on the last day of the June 2016 campaign because it had reached its spending limit.

In contrast, Vote Leave carried on, despite busting its limit two days before the vote – and was later found by the Electoral Commission to have broken the law.

Earlier this year, Vote Leave whistleblower Christopher Wylie also alleged the cheating won the support of enough voters, through precisely targeted online advertising, to sway the referendum result.

Friday’s case has been brought by a group of British expats in other EU countries, called UK in EU Challenge, which argues lawbreaking during the campaign means the result cannot be considered the “will of the people”.

The professor was asked to provide an expert’s report which Croft Solicitors, acting on behalf of the claimants, will seek to use as evidence in its case for a substantive hearing.

Carole-Anne Richards, one of the claimants, said the public had the right to expect the referendum to have been carried out “lawfully, free from corrupt and illegal practices”, adding: “This is clearly not the case here.

“We are very grateful to Professor Howard for his work in looking at Vote Leave Facebook advertising overspend and correlating that with voter behaviour.”

The group will argue that Brexit must be declared void and the notification of Article 50 quashed, because “various criminal offences may have been committed”.

It had been expected that any ruling would await the conclusions of the NCA probe, but it is now thought it will be fast-tracked – with less than four months until Brexit day.

Mr Banks could be given a two-year prison sentence if he is found to have “knowingly concealed” that an Isle of Man company was the source of up to £8m for Leave.EU – which would have been outlawed as a foreign donation.

Croft Solicitors wrote to the prime minister on 6 November asking her to “reconsider her refusal to take any action” over the lawbreaking exposed during the campaign and the announcement of the NCA investigation.