Scotland’s cities will suffer the brunt of the damage to be wrought by Brexit with billions of pounds wiped off the value of their economies.

A major new analysis has found Aberdeen - already shedding jobs as the oil price languishes - will be by far the hardest hit place in Britain by the decision to leave the European Union.

But experts have also calculated that Glasgow and Edinburgh, whose industries are more internationalised than the northern English rust belts which voted Yes in last year’s referendum, will also suffer disproportionately.

The Centre of Cities, a think tank, found none of Britain’s 62 major conurbations would benefit from Brexit, whether it is ‘hard or soft’.

In a ten-year forecast, they worked out that Aberdeen would fare worse than anywhere else in the UK by a substantial margin.

The city's £18bn-a-year- economy, they predict, will underperform by the the equivalent of 3.7 per cent of its entire annual output - the equivalent of around £500m at current prices - if the UK opts for a hard Brexit.

A softer Brexit, they said, will also mean the city's economy sag some 2.1 per cent.

Experts ranked Edinburgh sixth, just above London, on its hit parade of cities to do worst out of Brexit. The Scottish and English capitals, both of which voted against leaving the EU, are both heavily exposed to the kind of lucrative global financial services sectors most vulnerable to poorer trading conditions.

A spokeswoman for the Scottish Government said: "This report further confirms the damage which taking us out of the EU is likely to do to our economy – and the threat of an extreme Brexit, outside the Single Market and Customs Union will undoubtedly cause severe long-term economic damage, hitting jobs, growth and living standards."

SNP ministers want Scotland to stay in the single market and have come up with proposals, first mooted in The Herald, for a differentiated Brexit. These have, so far, been rejected by UK ministers.

The Centre of Cities, using analysis from the Centre for Economic Performance at the London School of Economics, measured predicted drags on city economies across the UK of two Brexit scenarios, soft and hard, meaning Britain joining or not joining a free trade area with the EU.

They forecast that, under a Hard Brexit, Edinburgh and Glasgow will respectively have overall economic output of 2.7 per cent and 2.4 per cent lower than they would have if Britain remained in the EU. Glasgow, they said, would lose 2.4 per cent, compared with remaining.

Conservative and Labour figures both now reject membership of the single market and customs union but aim for a free trade deal which would include non-tariff barriers.

This, characterised as a soft Brexit by the Centre for Cities, would have a penalty of 2.1 per cent of gross valued added for Aberdeen, 1.4 per cent for Edinburgh and 1.3 per cent for Glasgow.

The Centre for Cities said it was vital for the UK Government to get a deal as close as possible to the current one to reduce damage to this kind of level.

The think tank's chief executive, Andrew Carter, stressed richer - and Remain-voting areas - stood to lose most. He said: "Contrary to much of the received wisdom on Brexit, it is the most prosperous UK cities which will be hit hardest by the downturn ahead – but poorer places across the North of England and Midlands will find it tougher to adapt."

Mr Carter's team also stressed that high-added-value internationalised cities, most in the south of England or Scotland, while hardest hit, would also be best equipped to think of ways to handle the Brexit transition.

Aberdeen is so far ahead of other highly affected cities - such as the tech towns of the Thames Valley - that economists describe it as an outlier.

City leaders believe the North-East city, already buffeted by economic trends beyond its control, may have wider global links beyond the EU to help it limit damage.

Russell Borthwick, chief executive of Aberdeen and Grampian Chamber of Commerce, said: “These figures are a reflection of the global footprint that businesses in the Aberdeen city region currently have and the focus there has been on internationalisation.

"Clearly there are challenges associated with whatever type of Brexit outcome we see but we are hopeful that the technology, skills and innovation for which this area is renowned will stand us in good stead to see this as opportunity rather than a threat."

Shadow Scottish Secretary Lesley Laird MP said the new report showed

just how reckless the Tories’ Brexit gamble was."

Ms Laird - whose party has been under pressure to clarify its EU position north of the border, talked of a "jobs-first Brexit" and referred to "retaining the benefits of the single market and the customs union."

A UK Government spokeswoman said: "We are committed to a bold and ambitious Free Trade Agreement that works for the whole of the UK.

"The Government is engaging extensively with businesses and organisations across the country, and will continue this work throughout the exit process.

"Through the Government's modern Industrial Strategy we will look to build on the diverse strengths of all of the UK’s cities and regions."