By Sarah Young and Kylie MacLellan

LONDON (Reuters) - Britain's pro-European Union Liberal Democrats won a parliamentary seat previously held by the ruling Conservatives on Friday and said the surprise win was a rejection of a "hard Brexit" that would pull Britain out of the EU's single market.

The victory was in an area of London that voted strongly to remain in the EU in June's referendum. But the scale of the swing illustrated the deep divisions running through a country that voted 52-48 percent to leave the bloc.

It also underscored the risks faced by Prime Minister Theresa May as she plots Britain's EU divorce.

May spooked markets in October by suggesting she would take a hard line on Brexit by prioritizing border controls, but her government has shown signs of softening its stance since then.

Brexit minister David Davis said on Thursday that Britain would consider making payments to the EU to improve its access to the single market, giving sterling a bit of relief after falling sharply since June.

Friday's election victory by Liberal Democrat candidate Sarah Olney reduced May's already slim majority in parliament, which might be given a vote on whether to trigger the formal process of EU withdrawal.

Olney, who campaigned on a promise to vote against starting the Brexit talks, said the residents of the affluent Richmond Park and North Kingston area of southwest London, had sent "a shockwave" through the government.

"Our message is clear: we do not want a hard Brexit; we do not want to be pulled out of the single market; and we will not let intolerance, division and fear win," she said.

The government will appeal next week against a court ruling that parliament must vote on whether to trigger the divorce talks. Investors believe lawmakers, the majority of whom supported the Remain campaign, want to avoid a "hard Brexit".

"EUROPE IS WATCHING"

Brexit-supporting former minister Michael Gove said it would be a "profound mistake" to interpret the Richmond election result "as any sort of mandate to frustrate the will of the British people".

The constituency is not representative of much of the country.

But Liberal Democrat leader Tim Farron said a nearly a third of Leave-supporting Conservative voters in the seat had switched to his party.

"This is not just about Remain versus Leave re-run, this is about people trying to say to Theresa May, we do not like the extreme version of Brexit," he told BBC radio.

Remain-supporting Conservative lawmaker Anna Soubry said the win was "sensational", saying on Twitter: "politicians ignore #Remainers at their peril and you can forget #Hardbrexit".

The European Parliament's top Brexit negotiator, Guy Verhofstadt, also congratulated Olney via Twitter. "Europe is watching and we are proud," he said.

Olney beat the incumbent Zac Goldsmith with 20,510 votes to his 18,638, overturning the Conservatives' more than 23,000 majority in the 2015 national election. Goldsmith ran as an independent after quitting the Conservatives over the government's decision to expand nearby Heathrow Airport.

With all the main candidates opposed to the Heathrow expansion, the Liberal Democrats turned the by-election into a vote on the terms of Brexit. Goldsmith was a Leave supporter.

May's Conservatives, which did not field a candidate, said the result did not change Britain's Brexit strategy or its plans to invoke Article 50 of the EU's Lisbon Treaty to begin the withdrawal process by the end of March next year.

DISRUPTIVE

Since the June 23 Brexit vote, investors have watched for clues as to how the government will seek to maximize single market access while also curbing immigration from the EU.

The Liberal Democrats, junior partner in a coalition government with the Conservatives for five years before they were crushed in the 2015 general election, have said they want a second referendum on the terms of the Brexit deal.

"What this by-election shows is that it's a warning to all political parties as to potentially how disruptive this Brexit process is going to be for the regular practice of party politics," polling expert John Curtice told the BBC.

The Liberal Democrats held Richmond Park for 13 years until 2010. Their victory follows a strong second-place result for the party in an October by-election for a constituency vacated by former Prime Minister David Cameron.

May's Conservatives face another by-election on Dec. 8, after one of their lawmakers, Stephen Phillips, resigned in November citing "irreconcilable policy differences" with the government.

(Additional reporting by Kate Holton; Editing by Pravin Char and Giles Elgood)