Theresa May has warned that the future of European Union citizens living inside the UK is uncertain and their status will be part of any Brexit negotiations.

The Home Secretary, who has emerged as the clear front-runner in the Conservative Party leadership contest following the withdrawal of the former London mayor Boris Johnson, also told ITV’s Peston on Sunday there could be an upsurge in immigration before Britain officially leaves the EU.

And though Ms May said she wanted to “guarantee the position” for EU citizens currently living in the UK and British citizens living in EU countries, she admitted their future was up for negotiation.

“What's important is there will be a negotiation here as to how we deal with that issue of people who are already here and who have established life here and Brits who have established a life in other countries within the European Union.

“The position at the moment is as it has been, there's no change at the moment, but of course we have to factor that into negotiations.”

“As part of the negotiation we will need to look at this question of people who are here in the UK from the EU.”

It comes after Tim Farron, the Liberal Democrat leader, demanded that EU nationals residing in the UK are given complete assurances that they will have the right to stay in the UK indefinitely. The party, which has committed to standing in the next election on the platform of securing Britain’s place in the EU, added that the future status of these people is not clear beyond any renegotiation period, leading to uncertainty.

The favourites in the Tory leadership race Show all 5 1 /5 The favourites in the Tory leadership race The favourites in the Tory leadership race Theresa May The longest-serving Home Secretary in 100 years took a back seat in the referendum campaign. While backing Remain, she did not hit the campaign trail and delivered only a handful of speeches and interviews, and was critical of many aspects of the EU, particularly the European Convention on Human Rights. Hedging her bets allows her to now emerge as a ‘unity’ candidate, and she is said to have been building up her back-room staff in preparation for a leadership bid. She has the significant advantage of having served in one of the great offices of state, in a steady and competent manner that has won her many admirers within party and the civil service. At a time of great instability, it may be that she is viewed as steady hand on the tiller. Mrs May does however, lack the ‘star quality’ of a Boris Johnson and party members may doubt her ability to connect with ordinary voters PA The favourites in the Tory leadership race Michael Gove The Justice Secretary may be able to set himself up as ‘the thinking Tory’s Brexit candidate’. Made an enormous political and personal decision to back Leave, taking on his old friend David Cameron. He performed well during the TV debates, and will be an admired figure among Eurosceptic Conservatives. Along with Johnson, he will be hindered by the fact that he led a very divisive campaign, characterised by ‘blue-on-blue’ action. MPs may also judge that he lacks Boris Johnson’s wider appeal with the electorate. Possibly more likely that he will settle for being his new bosom buddy Boris’s Chancellor Getty The favourites in the Tory leadership race Stephen Crabb Highly-rated Work and Pensions Secretary, raised on a council estate, so could reach out to non-traditional working class Tory voters Getty Images The favourites in the Tory leadership race Andrea Leadsom Minister of State for Energy at the Department of Energy and Climate Change is one of the most prominent figures in the Leave campaign, seen to have performed well in TV debates Rex Features The favourites in the Tory leadership race Liam Fox British Conservative MP and former Secretary of State for Defence, as sources said he will stand for the leadership of the Conservative Party AFP/Getty

“There is real, and legitimate, upset and worry from European citizens across our country about their long-term status in the UK,” said Mr Farron. “Liberal Democrats will not stand by whilst our communities are divided by uncertainty. Regardless of the outcome of any negotiations with Europe around Brexit, EU citizens who have made Britain their home must be allowed to stay.

“To Europeans whose lives are now rooted in the UK my message is simple – the Liberal Democrats stand with you, and will speak for you. To the French family raising their children in Manchester, to the Polish mother working to pay her mortgage in Portsmouth, to the German graduate starting his business venture in Birmingham - the Liberal Democrats value you, we will stand by you and we will champion your future here in Britain.

“There are plenty of decent people who voted for Leave, who do not want to see Europeans who live in the UK in our communities forced to uproot their lives. There must be a cast iron guarantee that their futures can be in the UK, the country they now call home.

The Home Secretary also used the interview to reject any suggestion of her “coronation” as Tory leader due to a clear lead among her rivals. Ms May said she was not taking “anything for granted”, adding there is a need for the arguments to be heard by Tory members.

Recent polling has revealed that most Conservatives back the Home Secretary to succeed David Cameron – among party members, who will vote to decide the winner of the contest, some 46 per cent say she would make the best Prime Minister.

Ms May was also backed by 60% of Tory voters, with Mr Gove second on 10 points and Mrs Leadsom on six, according to the ICM poll for The Sun on Sunday.

Bitter recriminations over rival Michael Gove's decision to pull the rug from under Boris Johnson's leadership bid appear to have dented his prospects of taking on the Home Secretary in the final vote. In an attempt to destabilise Ms May's campaign, Mr Gove says that she lacks the moral authortty to lead the country because she campaigned against Brexit.

"If you are going to have a leadership election and the prime minister has chosen to stand down, then the logic is that you need to have someone who backed Brexit and believed in it and argued for it as you leader in these negotiations," he told The Sunday Times.

Former City worker Mrs Leadsom has likened herself to Margaret Thatcher and praised the late prime minister's ability to mix toughness with "personal warmth".

She also criticised any attempt to hand the leadership to Ms May.

"Some are suggesting the simplest way for the Conservative Party to move forward is some sort of "coronation" and that there should be no role for those who campaigned for Britain to leave the EU.

"I can't believe anybody would seriously consider this," she told The Sunday Times.

With levels of support stronger than the combined total of her four rivals, Ms May appears to be on course to take the keys to Downing Street. Ms May has also been backed by more MPs, who select the final two candidates to go on to the ballot paper, than any of the other candidates.

Although the poll puts Mr Gove, who has wider name recognition, ahead of Mrs Leadsom, bookies have slashed the odds on the junior minister making it through the knock-out stages in Parliament to go up against Mrs May in the head-to-head. The first round of voting to whittle down the field of runners is being held on Tuesday.

More than half of those polled – 55 per cent – by ICM were unable to give any view on Mrs Leadsom or Work and Pensions Secretary Stephen Crabb, who have lower profiles than the long-standing Cabinet ministers, and 42 per cent had the same problem with former frontbencher Liam Fox.

"The race to replace David Cameron might turn from a marathon into a sprint judging by these results. Theresa May is blasting out of the blocks and leaving her fellow competitors for dead,” ICM director Martin Boon told The Sun on Sunday.