The Downing Street 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.
"I hope our future Government will condemn far-right retweets by Donald Trump. They are abhorrent, dangerous and a threat to our society," Corbyn said.
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.
Also Read
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.
"Trump sharing Britain First. Let that sink in. The President of the US is promoting a fascist, racist, extremist hate group whose leaders have been arrested and convicted. He is no ally or friend of ours," added her fellow MP David Lammy.
Disclaimer: No Business Standard Journalist was involved in creation of this content