Theresa May's spokesman, James Slack, said the claim that the UK's signals intelligence agency GCHQ helped then-president Barack Obama eavesdrop on Mr Trump was "ridiculous".
"We've made clear to the administration that these claims are ridiculous and they should be ignored and we've received assurances that these allegations will not be repeated," he said.
"We have a close, special relationship with the White House and that allows us to raise concerns as and when they arise as was true in this case."
Representatives for the White House did not immediately reply to a request for comment.
Earlier, GCHQ had said in a rare public statement that the charge, made on Tuesday by Fox News analyst Andrew Napolitano, should be ignored.
"Recent allegations made by media commentator Judge Andrew Napolitano about GCHQ being asked to conduct wiretapping against the then-president-elect are nonsense," a spokesman said.
GCHQ never usually comments on criticism of its work beyond saying it always operates under a strict legal framework.
Mr Trump, who became President in January, tweeted earlier this month that his predecessor had wiretapped him during the late stages of the 2016 campaign.
- British PM Theresa May and GCHQ say wiretapping allegation should be ignored
- Spy agency issues rare public statement in response to claim it helped Barack Obama eavesdrop on Donald Trump
- US Senate Intelligence Committee finds "no evidence" that Trump Tower was under surveillance
- Trump "stands by" wiretapping claim, says White House spokesman Sean Spicer
The President has offered no evidence for the allegation, which an Obama spokesman said was "simply false".
White House spokesman Sean Spicer repeated the claim on Thursday that GCHQ was used by Mr Obama to spy on Trump Tower.
He told a news briefing that Mr Trump stood by his wiretap accusations.
His comments came after the Republican and Democratic leaders of the Senate Intelligence Committee said they saw no evidence to support Mr Trump's claim.
GCHQ, which monitors overseas electronic communications, is one of three main British spy agencies alongside the MI6 Secret Intelligence Service and the MI5 Security Service.
GCHQ has a close relationship with the US National Security Agency, as well as with the eavesdropping agencies of Australia, Canada and New Zealand in a consortium called Five Eyes.