The Downing Street statement said Britain First sought to divide communities through its use of "hateful narratives which peddle lies and stoke tensions".
"It is wrong for the president to have done this," the spokesperson said.
However, Downing Street said plans for a state visit by the US president remain in place.
The statement came soon after Britain's Opposition leader, Jeremy Corbyn, branded Trump's tweets "abhorrent and dangerous".
The Labour Party leader and many of his MPs took to social media soon after news emerged of Trump's retweets of inflammatory anti-Muslim videos by Britain First.
The first Trump tweet from Jayda Fransen, the deputy leader of Britain First, claims to show a Muslim migrant attacking a man on crutches. This was followed by two more videos of people Fransen claims to be Muslim.
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 they deem "the Islamification of the UK".
"UK Gov can't stay silent on Trump tweets. He is promoting woman convicted of hate crime from racist group here in UK. Disgraceful & dangerous," tweeted Labour MP Yvette Cooper.
The original video retweeted by Trump was shared by US conservative commentator Ann Coulter, who the US President follows.
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