The Lib Dem leader argued that the British people did not vote to leave the single market, and so should be given a vote on the final Brexit deal.
The Prime Minister will trigger Article 50 on March 29 and has insisted that Parliament will get a vote on the final Brexit deal.
Mr Farron claimed that the British people deserved to have a choice on the final deal as he urged Mrs May to re-think her decision of pulling the UK out of the single market.
Speaking to the BBC, he said: “I think the United Kingdom needs to look at trying to get the best possible deal for itself.
Tim Farron urged the Prime Minister to give the British people another referendum on Brexit
“In doing so it needs to be generous, not only in the things that it offers, but in its tone of language towards our European neighbours.
“After all, this is the biggest market on planet earth and whether we are in it or without it, we want to be trading alongside it.
“It’s foolish to think that somehow trade with New Zealand, Australia, or even the United States can match the enormous benefit of being in the single market.
“Which is why if I was in the position that Theresa May was in, I would not be giving up on membership of the single market.”
Brexit: Results of how the UK voted Mon, March 20, 2017
Much of the North East of the United Kingdom voted to leave the European Union including Sunderland, Gateshead, Darlington, Durham, Hartlepool, Middlesbrough, Stockton, Redcar and Cleveland, North Tyneside and South Tyneside, and Northumberland
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GREAT YARMOUTH: The town of Great Yarmouth on the East Coast of England voted by 72% to leave the European Union.
How is it right to impose it on the British people without them having a say
The 46-year-old Lib Dem then leader demanded the British people were given a referendum on the Brexit deal.
He added: “Fundamentally though, you rightly say, we don’t know what is going to come out of these negotiations, at all.
“Given we don’t know that, how is it right to impose it on the British people without them having a say.
“In the end, this deal will be settled, and it will either be signed off by the politicians, that is Theresa May’s intention, and Labour and Ukip agree with her.
“Or it will be signed of by the people on a referendum on the deal.
“That is what the Liberal Democrats strongly believe and we will spend the next two years saying so.”
Mr Farron finished by demanding both the UK and EU “behave like grown-ups” during the Brexit negotiations.
He said: “I can only affect what I say, Theresa May can only affect what she says, and she can find herself in a position where she may get a better deal, from the European Union, A – If she asks for one in the first place, i.e. don’t give up on being in the single market, and secondly if she doesn’t practise gunboat diplomacy on her fellow Europeans.”