The leader of the party hailed the result as a verdict on Mrs May's "UKIP-ish" take on Brexit
The Liberal Democrats in the UK have vowed to fight against a "hard Brexit" in the aftermath of the party's stunning victory in a by-election.
A buoyant Tim Farron, the Lib Dems' leader, said Prime Minister Theresa May must listen to calls to avoid a British exit from the EU that involves losing access to the single market.
The by-election took place in Richmond Park, with Sarah Olney overturning a massive Conservative majority of 23,000 to oust pro-Brexit Zac Goldsmith, who resigned in protest against Heathrow expansion and stood as an independent in the southwest London seat.
Mrs Olney said that the result paved the way for the British parliament to "override" the EU referendum result.
She said: "It does look now as if we can have a vote in Parliament that might override the referendum. And I will, obviously, be voting to Remain because that is always what I have believed."
Mr Farron hailed the result as a "historic moment for the country", and said it was a verdict on Mrs May's "UKIP-ish" take on Brexit.
He told Sky News that while one by-election result could not change governments, they can "change a Government's attitudes and direction".
Mr Farron said: "If Theresa May now listens to dozens of Tory MPs, with Liberal Democrats breathing down their necks, who are saying 'hang about, we don't want to leave the single market, we'll lose our seats if we do', it could well be that Theresa May changes her position and we end up with a referendum on the deal at the end.
"We at least end up with a soft Brexit, in which case, future generations of British people will have an awful lot to thank Sarah and the people of Richmond Park for."
The result was seized on by the European Parliament's lead Brexit negotiator, Guy Verhofstadt, who congratulated Ms Olney and said Europe "is watching".
Conservative MP and Remain campaigner Anna Soubry said the result was "sensational", writing on Twitter that MPs "ignore Remainers at their peril & u can forget #Hardbrexit".
When asked whether the result might influence Mrs May to soften her government's Brexit stance, a Downing Street spokesman said: "We had an election and we had a referendum.
"The referendum result was very clear and the majority of the country expressed an opinion for us to leave the EU.
"The message from the British people was loud and clear on 23 June that there is a desire for us to leave the EU.
"The Government is getting on with delivering that."
Asked whether the result might make the PM rethink her opposition to a second EU referendum, the spokesman replied: "No."