The Vote Leave campaign has accused David Cameron of being “knee deep in a conspiracy” to keep Britain in the EU, as letters emerged indicating the Prime Minister discussed the role big business could play in the Remain campaign before he had even completed his renegotiation deal with European leaders.

In a letter to Mr Cameron from Serco chief executive Rupert Soames, sent 11 days before the renegotiation deal was completed, and the EU referendum formally announced, the business leader refers to talks held with the Prime Minister earlier in the month.

He writes that, following up on the meeting, he is planning to contact FTSE 500 companies to urge them to mention the risks of Brexit in their annual reports.

At the time of the meeting and the letter, dated 8 February, Mr Cameron’s official position was that he could still campaign for a Leave vote if his renegotiation failed to secure the changes he wanted.

He told the House of Commons on February 3: “I am not arguing – and I will never argue – that Britain couldn’t survive outside the European Union…If we can’t secure these changes, I rule nothing out.”

What to believe about the EU referendum

However in the letter, seen by the Daily Mail, Mr Soames states: "There were two points I thought I might follow up on. The first is how to mobilise corporates to look carefully at the risks Brexit represents.

"I am working with Peter Chadlington and Stuart Rose [head of the Britain Stronger in Europe campaign) with a view to contacting FTSE 500 companies who have annual reports due for publication before June and persuading them that they should include Brexit in the list of key risks. All public companies are required to set out in their annual report an analysis of key risks."

Labour MP Gisela Stuart, chair of the Vote Leave campaign, said the Prime Minister had “serious issues” to answer.

“We now know he has been doing deals with businesses to exaggerate the risk of a vote by the UK to leave the EU,” she said. “He must now tell us urgently how many businesses he cut secret deals with? Who are they and what were they promised in return?”

Downing Street said it did not comment on leaked documents.

Many Westminster observers doubted at the time that the Prime Minister was seriously considering backing a Leave vote, but the timing of the leaked letter will be embarrassing to the Remain campaign, coming a day after George Osborne mocked Brexit campaigners as conspiracy theorists.

What has the EU ever done for us? Show all 7 1 /7 What has the EU ever done for us? What has the EU ever done for us? 1. It gives you freedom to live, work and retire anywhere in Europe As a member of the EU, UK citizens benefit from freedom of movement across the continent. Considered one of the so-called four pillars of the European Union, this freedom allows all EU citizens to live, work and travel in other member states. What has the EU ever done for us? 2. It sustains millions of jobs A report by the Centre for Economics and Business Research, released in October 2015, suggested 3.1 million British jobs were linked to the UK’s exports to the EU. What has the EU ever done for us? 3. Your holiday is much easier - and safer Freedom to travel is one of the most exercised benefits of EU membership, with Britons having made 31 million visits to the EU in 2014 alone. But a lot of the benefits of being an EU citizen are either taken for granted or go unnoticed. What has the EU ever done for us? 4. It means you're less likely to get ripped off Consumer protection is a key benefit of the EU’s single market, and ensures members of the British public receive equal consumer rights when shopping anywhere in Europe. What has the EU ever done for us? 5. It offers greater protection from terrorists, paedophiles, people traffickers and cyber-crime Another example of a lesser-known advantage of EU membership is the benefit of cross-country coordination and cooperation in the fight against crime. What has the EU ever done for us? 6. Our businesses depend on it According to 71% of all members of the Confederation of British Influence (CBI), and 67 per cent of small and medium-sized enterprises (SMEs), the EU has had an overall positive impact on their business. What has the EU ever done for us? 7. We have greater influence Robin Niblett, Director of think-tank Chatham House, stated in a report published last year: “For a mid-sized country like the UK, which will never again be economically dominant either globally or regionally, and whose diplomatic and military resources are declining in relative terms, being a major player in a strong regional institution can offer a critical lever for international influence.

Ms Stuart added: “George Osborne accused the Leave campaign of inventing conspiracies. Now we see that David Cameron is knee deep in one.”