Votes are being counted in the Richmond Park by-election where former Conservative MP Zac Goldsmith is facing a concerted Lib Dem bid to unseat him.
Turnout at the polls came in at 41,367, or 53.6%, as Mr Goldsmith defended a majority of 23,015 at last year's general election.
Mr Goldsmith quit as Tory MP in protest at the Government's plans to build another runway at Heathrow, but Lib Dems tried to switch the focus of the campaign to Brexit in the staunchly Remain constituency.
The defeated Tory London mayoral candidate stood on an independent, anti-Heathrow expansion ticket, as the Lib Dems poured resources into the contest to boost their standard bearer Sarah Olney.
In the final hours of campaigning, the party hit the streets with Bob Geldof, who attacked Mr Goldsmith, an old friend, for being a failure and chanted "Zac is crap" while posing for pictures.
The singer joined Ms Olney, an accountant working at the National Physical Laboratory in Teddington, who joined the party in May 2015, to chat to voters.
Neither the Tories nor Ukip put up candidates to stand against Mr Goldsmith.
Some Labour MPs urged their party to avoid contesting the by-election to give the Lib Dems a better chance of winning, but writer, broadcaster and railway historian Christian Wolmar represented the party.
The Greens, who called for a ''progressive alliance'' against Mr Goldsmith, did not run a candidate.
Eight candidates also contested the seat, including Fiona Syms, the ex-wife of Tory MP Robert Syms (Poole). She stood as an independent opposed to Mr Goldsmith but has said she would seek to join the Conservatives if elected.
Alistair Carmichael, the Lib Dem spokesman for home affairs, said the party was "not at all confident of anything other than we are three or four hours away from the result".
"What is clear though is that having started 23,000 votes behind Zac Goldsmith - it is going to be an awful lot closer than that," the Orkney and Shetland MP added.
"What we have been saying for the last few weeks is that this was an election that was about the Brexit vote and that Zac Goldsmith is very much on the wrong side of public opinion in his own constituency, (which) appears to be reflected in some of the early returns here tonight."
He told the Press Association that there had been campaigning weekends where there were up to 800 Lib Dem activists knocking on doors and canvassing for votes across the constituency.
Mr Carmichael said the party's "strong national message" on stopping Brexit has had a "strong resonance" on the door steps of Richmond Park where 70% voted to remain.
"Theresa May has no respect for their views and if they're going to have a voice in politics it is going to come from the Liberal Democrats - that is the significance of tonight," he added.
In terms of the Lib Dems' popularity since they were obliterated at the 2015 general election, Mr Carmichael said they had gained local council seats for the party since May and there has been a "massive" increase in party membership.
"It has not been an easy few years to be a Liberal Democrat, but the fightback is definitely on."