A big red bus emblazoned with the words “we send the EU £350m a week, let’s fund our NHS instead” is credited as being decisive in Britain’s vote to leave the EU last year.

It promised — in absolute terms — financial gains for the British public if they voted to leave, a stark counterweight to a majority of economists who warned that a departure would hurt Britain. The pre-referendum estimates of the long-term pain ranged from a hit to the economy of 1 per cent to 9 per cent of national income — an annual loss of gross domestic product of between £20bn and £180bn compared with remaining in the EU.

The Leave campaign won the battle of the slogans, and the referendum. But who is winning the economic argument? Almost 18 months on from the Brexit vote and with 15 months of detailed UK data, it is now possible to begin to answer that important question.

Economists for Brexit, a forecasting group, predicted that after a leave vote growth in GDP would expand 2.7 per cent in 2017. The Treasury expected a mild recession. Neither proved correct. The 2017 growth rate appears likely to slow to 1.5 per cent at a time when the global economy is strengthening.

According to economists such as Robert Chote, chairman of the independent Office for Budget Responsibility, which produces the official government forecasts, a more pressing question is to assess the impact compared with what would have happened had the vote gone the other way. “Many PhDs are going to be written on the impact of Brexit over the years to come,” he says.

This work has started, and includes a range of estimates calculated by the Financial Times suggesting that the value of Britain’s output is now around 0.9 per cent lower than was possible if the country had voted to stay in the EU. That equates to almost exactly £350m a week lost to the British economy — an irony that will not be lost on those who may have backed Leave because of the claim made on the side of the bus.

Jonathan Portes, professor of economics and public policy at King’s College London and one of the academics leading publicly funded research into the effects of Brexit, says: “The conclusion that, very roughly, Brexit has already reduced UK growth by 1 per cent or slightly less seems clear.”

Companies are becoming more vocal over the economic hit, blaming the government’s slow handling of the Brexit negotiations for a weaker business climate. In October, the International Monetary Fund highlighted Britain as a “notable exception” to an improving global economic outlook, while the OECD, the Paris-based club of mostly rich nations, has raised concerns about “the ongoing slowdown in the economy induced by Brexit”.

Thomas Sampson and colleagues at the London School of Economics have examined the direct effect of sterling’s depreciation since the EU referendum on prices and living standards. With the pound falling about 10 per cent following the June 2016 result, inflation has risen more in Britain than in other advanced economies. It started with petrol prices and spread to food and other goods, pushing overall inflation up from 0.4 per cent at the time of the referendum to 3.1 per cent last month .

When looking at prices, depending on the level of import exposure of different goods and services, the LSE study estimates that the Brexit vote directly increased inflation by 1.7 percentage points of the 2.7 percentage-point rise in the 12 months after the referendum. And with wage inflation stuck at just over 2 per cent, “the increase in inflation caused by the Leave vote has already hurt UK households”, Mr Sampson says.

He calculates that “the Brexit vote has cost the average worker almost one week’s wages”, but adds the figure could be higher or lower if a complete evaluation of the economic impact was applied rather than just the initial squeeze on incomes from leaving the EU.

Other effects are more apparent. Business investment grew at an annual rate of 1.3 per cent in the third quarter, compared with a March 2016 official forecast for annual growth of 6.1 per cent for the whole of 2017. Exports, boosted by sterling’s depreciation, have proved more resilient. The OBR now expects a 5.2 per cent rise in the volume of goods and services sold abroad in 2017 compared with a pre-referendum prediction of 2.7 per cent.

Net migration to the UK from the EU fell by 40 per cent in the first 12 months after the vote. Professor Portes last year predicted an ultimate decline of between 50 and 85 per cent on net migration levels before the referendum. “Arithmetically, this reduction [of 40 per cent] of net EU migration translates into a reduction in growth of 0.1 to 0.2 per cent,” he says.

Economists working to estimate the overall Brexit impact on the economy need to build a counterfactual scenario — an imagined world in which Britain had voted to remain in the EU — to compare that with Britain’s economic performance since the vote. The counterfactual cannot be known for certain but it is possible to take a number of approaches, in three broad categories.

Chart showing UK economic performance relative to the G7 © FT

The first is to compare recent UK economic performance with its past. A worse performance than the UK has achieved over long historical periods or in recent years would support the view that the vote has hurt economic performance. But a shortcoming of this approach is that if the past year was always likely to be rather weak, this method could suggest a Brexit hit when there was none.

Comparing the UK performance with that of other countries is another option. Using its normal position in the G7 league table of leading economies is one possible technique, as is contrasting UK performance with the average of similar economies. A more sophisticated approach is to use a statistical algorithm to devise a historically accurate set of comparator countries, a method recently performed by a group of academics from the universities of Bonn, Tübingen and Oxford. These geographical techniques often smooth out concerns that the recent period might be unusual, but they are vulnerable to variations in other countries, such as a sudden boom in the eurozone that Britain was never likely to match.

A third tactic is to look at forecasts made for Britain’s economy before the referendum on the basis of staying in the EU and compare the actual outcome with these prior forecasts. Its weakness is that there was a wide range of pre-referendum forecasts, while its strength is that the figures reflect the best knowledge available at the time.

Net migration to the UK from the EU fell by 40 per cent in the first 12 months after the Brexit vote.

Jagjit Chadha, director of the National Institute of Economic and Social Research, says each of the methods are reasonable for generating an estimate of the impact of Brexit so far. “We can’t know how the [UK] economy would have responded to the news over the past 18 months, but there have not been any large shocks and the rest of the world has done slightly better than we thought likely a year ago.”

The results vary according to the comparisons made, but all show the UK economy has been damaged even before it formally leaves the EU on March 29 2019.

When the past five quarters are judged against the UK’s historical average growth rate, the 1.9 per cent expansion in GDP achieved between the second quarter of 2016 and the third quarter of 2017 is lower than history would suggest is normal for the UK economy.

Depending on the period of comparison chosen, the UK economy would normally have been expected to expand by between 2.5 per cent and 3.2 per cent over the same period. The lower end of the range comes from more recent history, such as the average since a Conservative-led government came to office in 2010, while the upper boundary reflects Britain’s long-term performance in the 30 years before the financial crisis. The hit to the economy on this comparison is between 0.6 per cent and 1.2 per cent of national income.

Geographical comparisons produce a similar conclusion. Britain’s year-on-year growth rate tended to be close to the G7 upper range of outcomes over the past 25 years. Had that performance continued, British GDP would have grown 2.9 per cent since the referendum. The statistical algorithm produces a significantly larger estimate of what would have been possible, suggesting Brexit has already removed 1.3 per cent from GDP since the vote.

This equates British performance to a weighted average of other countries, with the US, Canada, Japan and Hungary having the largest weights. Asked whether it was reasonable to judge the UK’s performance against that of Hungary, Professor Moritz Schularick of Bonn University says, “like the UK, Hungary is a European economy and integrated into the production chains, but remained outside the eurozone with a floating exchange rate and therefore could use monetary policy more aggressively after the crisis”.

Estimates using pre-referendum forecasts provide a range within almost the exact same boundaries — between 0.6 per cent of GDP and 1.1 per cent. The larger figure is based on analysis from Economists for Brexit, which initially predicted strong growth after the vote.

Professor Patrick Minford, who carried out the forecasts for the group, blames “Office for National Statistics productivity estimates, [which] are not convincing because they have made no real attempt to estimate the growth in quality of services, such as in education and healthcare”. But all of this was known before the referendum.

Companies have been critical of Theresa May's government saying that delays in talks with the EU have hit business

Overall, 14 different counterfactuals estimated by the FT and others give a range of a hit between 0.6 per cent of national income and 1.3 per cent, with an average of 0.9 per cent. With national income of £2tn in the year ending in the third quarter of 2017, it means the UK is likely to be producing £18bn less a year than would have been reasonable to expect and this is directly attributable to Britain’s decision to leave the EU. That is just short of £350m a week.

Brexit-supporting economists say the figures are reasonable. Julian Jessop, head of the Brexit unit at the Institute of Economic Affairs, says: “Lots of sensible Brexiters accept there will be a short-term hit and it is unarguable that the economy is weaker than it would have been, I would say between 0.5 and 1 per cent weaker. As for the longer term, it’s all to play for. Brexit creates lots of opportunities, it is for the government to make the most of them.”

In the referendum campaign the big red bus was making a different comparison, an incorrect one, about the budgetary costs of the EU to Britain. It suggested Britain contributes almost £18bn a year to the budget, when the net cost in 2016 was calculated by the Treasury to be £8.6bn. And this leaves one last comparison that it is possible to make.

Paul Johnson, director of the Institute for Fiscal Studies, says that “for every 1 per cent of GDP you lose, that’s getting on for £10bn a year of foregone tax revenues”. If 0.9 per cent of GDP has been lost over the five quarters for which data exists, there has already been a £9bn hit to the public finances. So even before the UK has left the EU, the referendum result is costing the UK government more than can possibly be recovered by ending net contributions to Brussels.

Inflation has risen more in Britain than in other advanced economies since the Brexit vote rising from 0.4 per cent at the time of the referendum to 3.1 per cent in November