Trump shared three posts by the group’s deputy leader, including unverified footage purporting to show Muslims committing crimes.
British Prime Minister Theresa May’s spokesman said Britain First used “hateful narratives which peddle lies and stoke tensions”, BBC reported on Wednesday.
Labour’s Jeremy Corbyn called the retweets “abhorrent” and “dangerous”.
Britain First was founded in 2011 by former members of the far-right British National Party (BNP).
The group has grabbed attention on social media with controversial posts about what it deems “the Islamification of the UK”.
It has previously put up members to run in European elections and by-elections on anti-immigration and anti-abortion policies, but has yet to secure any seats.
The first tweet, from deputy leader Jayda Fransen, claims to show a Muslim migrant attacking a man on crutches.
This was followed by two more videos of people Ms Fransen claims to be Muslim.
White House spokeswoman Sarah Sanders said May and other world leaders knew the videos highlighted “real threats that we have to talk about”.
“Whether it’s a real video, the threat is real,” she added.
However,Trump’s tweets — shared with his 43.6 million followers — prompted a wave of criticism in the UK.
Corbyn tweeted: “I hope our government will condemn far-right retweets by Donald Trump. They are abhorrent, dangerous and a threat to our society.”
Veteran Tory MP Nicholas Soames said Trump had finally proved he is “wholly unsuited” to the role of president.
Meanwhile, fellow Conservative MP Nadhim Zahawi has written a letter to Trump urging him to delete the retweets
Speaking in the Commons, Labour MP David Lammy accused Mr Trump of “promoting a fascist, racist, extremist hate group”.
Fellow Labour MP Stephen Doughty said the videos were “highly inflammatory”, while his colleague Yvette Cooper, a former shadow home secretary, said Mr Trump had given Britain First a “huge platform”.
Theresa May is currently on an overseas trip, but both Doughty and Cooper asked the home secretary or foreign secretary to make a statement on the government’s behalf.
Both declined, but later a Downing Street spokesman said: “British people overwhelmingly reject the prejudiced rhetoric of the far right which is the antithesis of the values that this country represents – decency, tolerance and respect.”
He added: “It is wrong for the president to have done this.”
Foreign Secretary Boris Johnson later tweeted that Britain First was “a divisive, hateful group”, while Sajid Javid, minister for communities and local government, said Trump was “wrong and I refuse to let it go and say nothing”.