Tim Farron and Andrew Neil are involved in a fiery debate
Mr Farron, who has said his party would give voters a second referendum once the outcome of the Brexit negotiations is known, indicated he would campaign for the UK to remain in the EU were that to come about.
"I cannot see any chance of us getting a better deal than the one we have now," he told BBC1's The Andrew Neil Interviews.
"The deal we've got now is membership of the European Union, the deal we have now is membership most fundamentally of the single market, and then we have the op-outs.
"We have the fact that we have the rebate, we have exemption from Schengen. We don't have open borders."
During the course of the half-hour interview, Mr Neil repeatedly complained at what he said was the Lib Dem leader's refusal to answer direct questions, at one point accusing him of "filibustering".
When Mr Neil sought to press him on whether he would actually campaign for Remain in a second referendum, the presenter accused Mr Farron of trying to put him off his stride.
"You're not going to heckle me out of this. I will ask my questions. In the second referendum you will campaign … to reject any deal that Mrs May does?" he demanded.
Mr Farron replied: "I will campaign in that referendum on the basis of what's best for Britain. My view is I cannot see how Theresa May will be able to get a deal better than the one we currently have."
Here Express.co.uk gives you updates and latest breaking news as the interview aired on BBC..
7:29pm: And in one final blow during his final question Neil asks "why has your campaign gone so badly?" to which Farron retorts: "The Lib dems are doing extremely well."
7:28pm: Andrew Neil has stuck the knife in saying the Lib Dem manifesto was a "waste of time"
7:27pm: Farron has also ruled out plans for a coalition following the result of the General Election because of Theresa May and Jeremy Corbyn's plans to take Britain out of the single market.
He said the "biggest issue of the day" was access to the European market.
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7:25pm: The Lib Dem leader insists "we have looked at evidence" when quizzed on why he is aiming to legalise cannabis before admitting he wouldn't want his children to smoke the class B drug.
He says the party employed a team of experts to look into the legalisation of the drug, and plans to regulate the market will "minimise harm to the vulnerable and to maximise harm to criminal gangs".
He told Neil: "I wouldn't propose to do something controversial like this if the evidence didn't suggest that all of our children would be more safe than they currently are and the criminal gangs under more threat then they currently are. Let's follow the evidence."
Farron says he wouldn't want his kids to smoke cannabis
7:22pm: Farron is being griled on why he is proposing to rase income tax, despite saying working people's living standards are falling.
He hits back saying: "If you want the best NHS and care system in the world, you have to pay for it.
"It's the price of a cup of coffee a week for most people."
7:18pm: Neil has put the Lib Dem boss on the spot over his support for repealing measures such as a crackdown on encryption.
Farron pledged to spend £300million more on the police, suggesting the security services “have the powers that they need, but what they need are the resources to make use of them”.
7:15pm: Andrew Neil is now raising his voice: "This is how it works: I ask questions and you answer the questions, My question is quite simple. Mr Farron you are not answering.
"You are not going to heckle me out of this."
He asks: "In the second referendum you will campaign to reject any deal that any Mrs May does?
To which Farron says he cannot "imagine a deal that is better than the one we've got now".
7:12pm: The Lib Dem boss defended his party's call for curbs on surveillance powers used by the police and security services, saying: "We need to make sure that we don't have knee-jerk responses to the kind of outrage that we had last Monday."
7:11pm: Farron says "Britain should have final say on destination" to which Neil interrupts saying "you would tell them to Remain. Mr Farron, I am not going to argue with you on this. "
But Farron hits back: "I do respect the outcome of the referendum and I, nevertheless, feel a sense of real concern that in this country if you stand by your principles, if you question whether Theresa May is making the right choices, and Jeremy Corbyn of course backed her in that, then you are dismissed as a saboteur or a Remoaner."
7:08pm Andrew Neil blasted Tim Farron for calling himself a Eursceptic and a Remaoner saying "You are no Eurosceptic Mr Farron". He snipes: "you can't have it both ways".
7:03pm: Tim Farron starts off the debate by accusing Theresa May of "giving up on the most important aspect of negotiations" in terms of the single market.