The cost of Brexit to the British economy is running at £40bn a year and a damaging no-deal scenario could force an emergency cut in interest rates, according to a Bank of England rate-setter.

Gertjan Vlieghe, a member of the Bank’s monetary policy committee, said that since the vote in June 2016, the economy had lost about 2% of GDP compared with a scenario where there had been no significant domestic economic events.

The cost to Britain is currently £40bn a year, or about £800m a week of lost income, he said. Since the referendum, the UK’s economic growth has slowed while the rest of the world has recorded one of its strongest periods for growth of the past decade.

Vlieghe’s estimate for the weekly cost of Brexit so far is more than double the £350m the Leave campaign claimed could be saved on EU membership fees and instead spent on the NHS. The claim, emblazoned on the side of the campaign’s battlebus, became a key focus for debate in the run-up to the vote.

Vlieghe said in London on Thursday: “That 2% of GDP is not trivial, that’s £40bn or if you prefer it in bus units, it’s £800m a week.”

The Bank has calculated that the cumulative total of lost GDP since 23 June 2016 is £55bn.

He said business investment in Britain had been stuck around zero, with a drop of 3.7% in 2018, despite an upswing worth about 6% annually in the rest of the G7. Consumer spending also slowed as households came under pressure from higher prices, sparked by the sharp fall in the value of the pound straight after the Brexit vote.

“It is very unusual for investment to shrink that much when the rest of the world is doing pretty much just fine, until at least recently.

“UK growth in the past two years has been weaker than we would have expected based on the performance of the global economy alone,” he said. “Based on what happened in the rest of the world we would have expected UK growth to accelerate but actually it slowed.”

Several estimates have been made before to quantify the cost of the Brexit vote. Mark Carney, the Bank’s governor, has previously said the vote cost households about £900 each in lost income. There are also various estimates for the potential hit from Britain crashing out without a deal on 29 March.

Threadneedle Street estimates the worst-case disruptive scenario could spark a slump into a recession with worse consequences for Britain than the 2008 financial crisis, while the Treasury estimates that all Brexit options are worse for the economy than remaining in the EU.

Vlieghe, an independent economist on the Bank’s nine-member MPC, said the magnitude of the potential negative hit to the economy was uncertain, particularly over the long term.

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While he said there was an important democratic debate on the possible trade-offs between the political and economic consequences of Brexit, he added that leaving the EU without a deal could warrant an emergency cut in interest rates.

“In the case of a no-deal scenario I judge that an easing or an extended pause in monetary policy is more likely to be the appropriate policy than a tightening,” he said.

However, should Britain secure a smooth Brexit deal, the world economy manage to avert a further slowdown and inflationary pressure in Britain rise, he said it would be appropriate for the Bank to raise rates around once per year.

• This article was amended on 14 February 2019 to clarify the current annual cost to the UK economy.