BREXIT will take “at least five years” because of its staggering complexity and the burden it will place on Whitehall, the former head of the civil service predicted yesterday.

Lord Kerslake said he would be “amazed” if the UK’s withdrawal from the European Union was completed in 2019, in line with the Westminster’s current timetable. He suggested 2021 was the earliest realistic date – beyond the next general election.

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He was backed up by Sir John Elvidge, the former top civil servant in the Scottish Government, who said the UK’s exit from Europe was “probably a couple of years further out than 2019”.

Such a delay would anger millions of Out voters and enrage pro-Brexit Tory MPs, many of whom were furious last week when it was reported Brexit might slip from the first to the second half of 2019. Both mandarins were speaking at the annual Festival of Politics at Holyrood.

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Lord Kerslake, the head of the home civil service from 2012 to 2015, said of Brexit: “I think it’s going to be an enormous challenge. One, it will be a lot more complex and take a lot more time than people think it will...People talk about 2019, I would be amazed if we had completed the process by then. The second reason it’s going to be incredibly hard is that we don’t just have a political crisis, we have a constitutional crisis in this country, and not just Scotland. It raises a whole set of issues about how the UK operates.

“The final issue is that it’s not the only issue we face. We face a very fragile global economy… and I think we could be in for some quite rocky economic times. We’re going to have to deal with multiple challenges.”

Speaking to the Sunday Herald afterwards, he added: “I don’t believe we will have completed the process by 2019. I think there will still be big issues being resolved. I think it’s at least five years away, maybe longer. All this talk of it being a two-year process is optimistic.”

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Sir John, Scottish permanent secretary from 2003 to 2010, said the problems facing the Scottish, Welsh and Northern Ireland governments were “more acute” than for Westminster, as they would have to cope with the same Brexit headaches with a fraction of the civil servants.

He said: “Normally one spreads work over time, but the nature of Brexit means… it may be necessary to concentrate work in quite a tight period. That will be a huge capacity challenge.

“Particularly when you bear in mind it’s the same timeframe in which the Scottish Government is absorbing increased fiscal responsibility, responsibility for welfare – challenges that would have stretched the capacity that we have even without Brexit.

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“It’s a bit against the spirit of the times, but more civil servants is the answer.”

Theresa May has indicated she will start the Brexit process next spring by triggering the two-year Article 50 withdrawal.

However there remains huge uncertainty over what Brexit means in practice, made worse by squabbling among the three Brexiteers – Foreign Secretary Boris Johnson, International Trade Secretary Liam Fox, and Brexit Secretary David Davis. Kerslake added. “Until you know what your ask is, you’d be unwise to trigger a process.”

SNP Europe spokesman Stephen Gethins said: “These are worrying comments from Sir John Elvidge and Lord Kerslake – and a stark warning for Theresa May, who has so far failed to provide any details of how the UK will navigate Brexit. We must now hear her plans. The UK government must also ensure the devolved nations are not left short-changed and have the right resources for what lies ahead.”

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A spokesperson for the First Minister added: “The fact it is being suggested by such well-placed observers that the Brexit process could be so long and drawn out just lays bare the total lack of planning by the Tories. But that failure by Westminster will not stop us doing all we can to protect Scotland’s place in Europe.”

A spokesperson at the Department for Exiting the European Union said: "The country voted to leave the European Union, and the Government has been very clear that we are now going to get on with making a success of Brexit - getting the best deal for Britain. "