The contest is taking place following the death of former Cabinet minister James Brokenshire.
The Conservatives expect to retain the constituency despite a bruising few weeks for Boris Johnson’s administration over allegations of sleaze, claims that lockdown rules were broken in No 10 and the emergence of the Omicron coronavirus variant.
Mr Brokenshire died from lung cancer in October and local Tory councillor Louie French is the bookmakers’ firm favourite to succeed him.
Mr Brokenshire held the south-east London seat with a majority of almost 19,000 at the 2019 general election.
A string of senior Tories, including the Prime Minister, have visited the constituency during the by-election campaign, with Transport Secretary Grant Shapps among the MPs bolstering the effort to get out the vote on Thursday.
But Labour also had a high-profile on the streets of Old Bexley and Sidcup, with shadow chancellor Rachel Reeves and her sister and shadow solicitor general Ellie among those knocking on doors on polling day on behalf of candidate Daniel Francis.
As polls closed Ellie Reeves said: “This seat has always been a safe Tory seat and we don’t expect that to change tonight.
“However, people are increasingly fed up of the Prime Minister’s broken promises – on tax rises, social care and NHS waiting lists. Patience is wearing thin with Boris Johnson.
“We’ve run a positive campaign and people have been open to hearing Labour’s offer, but to win this was never within reach for us.”
Other candidates include Simone Reynolds for the Lib Dems, Jonathan Rooks for the Greens, and Reform Party leader Richard Tice.
The constituency has been held by the Conservatives since its inception in 1983, and in its previous incarnations since the 1950s, with former prime minister Edward Heath among those to represent it.