The Conservatives have insisted the Old Bexley and Sidcup by-election was a “good result”, despite the party’s majority in the traditionally blue seat taking a knock.

But Labour has said Boris Johnson should be “worried” by the outcome, arguing that “more and more people are concluding that Keir Starmer would make a better prime minister of this country”.

Tory Louie French became the UK’s newest MP following the poll on Thursday, which was triggered by the death of former Cabinet minister James Brokenshire.

Mr French took more than half the votes in the contest, but a turnout of just 34% meant the Conservatives’ majority was slashed from almost 19,000 to 4,478.

The party’s share of the vote fell from 64.5% – secured by Mr Brokenshire in 2019 – to 51.5%. Labour, meanwhile, pointed to a 10% swing in their favour.

However, Conservative Party chairman Oliver Dowden said on Friday that he is “really not terribly worried about Labour”, despite the improved performance by the Opposition.

Mr Dowden told Sky News: “This is a good result for a governing party mid-term.

“As you well know, governing parties shouldn’t expect to do well mid-term. We actually secured over 50% of the vote in Bexley. I pay tribute to our excellent candidate and the campaign team there that secured that result.

“This idea that Labour have made some surge ahead is really for the birds. They’ve actually got about the same vote share as they secured under Jeremy Corbyn in 2017.

“Keir Starmer couldn’t even be bothered to turn up to the by-election, so I am really not terribly worried about Labour.”

Asked how allegations of sleaze might have affected the Tories’ performance, Mr Dowden said: “Of course people have concerns mid-term with any government’s performance. And of course people have been concerned about what’s happened over the past couple of months.

“I actually think it’s tribute, contrary to a lot of expectations, to the campaign that has been fought by Louie French, by the excellent team down there, that we secured 50% of the vote.

“Now, what I take from that is that the Government has to focus and get on with delivery.”

But Labour’s national campaign co-ordinator, Shabana Mahmood, said the Prime Minister should be “worried” by the outcome.

Ms Mahmood, MP for Birmingham Ladywood, said if the result was replicated in a general election, Labour would be “within touching distance” of a majority government.

“The Prime Minister should be worried because, even by by-election standards, a 10.3% swing towards the Labour Party in such a strong Tory area, if that was replicated at a general election, that would put us within touching distance of a majority Labour government. So I take a lot of heart from that result,” she said.

She added: “For us it means, certainly those conversations that I had, that more and more people are taking a second look at the Labour Party and more and more people are concluding that Keir Starmer would make a better prime minister of this country.

“So, as I say, I take great heart from that, this was true blue Tory heartlands, and a 10.3% swing is an excellent result for us.”

The by-election took place against a difficult backdrop for the Tories, after weeks of allegations about sleaze, Mr Johnson’s chaotic speech to the Confederation of British Industry, claims that lockdown rules were broken in No 10 last Christmas, and the imposition of coronavirus restrictions following the emergence of the Omicron variant.

But Mr French insisted it was local issues that dominated the campaign.

“My focus will now be delivering on those promises that I made during the campaign – get our fair share of London’s police officers, securing more investment for local schools and hospitals, protecting our precious green space,” he said.