In a tweet from the Prime Minister’s official Twitter account, Ms May said: “Our thoughts and prayers are with #Charlottesville. The UK stands with the US against racism, hatred and violence.”
Labour leader Jeremy Corbyn echoed this sentiment, saying: “My thoughts are with those killed and injured in #Charlottesvile standing up to racism and hatred.”
Donald Trump belatedly condemned white supremacist groups that took part in violence scenes, but only following widespread criticism after he initially spoke out against hatred on “many sides”.
A ‘Unite the Right’ demonstration over the removal of a Confederate statue in the usually quiet, liberal-leaning university town of Charlottesville attracted hundreds of members of neo-Nazi groups and several members of the Klu Klux Klan.
The white-supremacist groups clashed with counter protesters, with pepper spray reportedly used by both sides, fist fights breaking out and bottles thrown.
A car slammed into a crowd of counter-protesters, killing a 32-year-old woman named as Heather Hayer and injuring at least 25 others. James Fields, 20, from Ohio, has been charged with murder.
Another 15 people were injured in street fighting, according to local hospital reports.
A police helicopter monitoring events on the ground also crashed, killing the two officers on board.
Charlottesville, Virginia Protests
Members of Congress from both the Democratic and Republican parties criticised Mr Trump’s first response, claiming his comments were muted and failed to place the blame with those responsible.
“Mr President – we must call evil by its name,” said Republican Senator Cory Gardner, chairman of the National Republican Senatorial Committee.
The founder of Daily Stormer, an American white-supremacist website which describes itself as “alt right”, welcomed the fact that Mr Trump “outright refused to disavow” the Unite the Right protest.
“People saying he cucked are shills and kikes,” said the site’s editor Andrew Anglin.
“He did the opposite of cuck. He refused to even mention anything to do with us. When reporters were screaming at him about White Nationalism he just walked out of the room.”
Some Democrats suggested that Mr Trump was unwilling to alienate the racist portion of his voter base as he received the backing of many “alt-right” websites during his bitterly fought election campaign against Hillary Clinton.
Charlottesville Mayor Michael Signer said he was upset the white nationalists had descended on his town and blamed Mr Trump for inflaming racial prejudices during his presidential campaign last year.
“I’m not going to make any bones about it. I place the blame for a lot of what you’re seeing in America today right at the doorstep of the White House and the people around the President,” he said.
Following accusations the President, usually a prolific tweeter, had been slow to comment at all on the violence and had then been vague in his initial comments, the The White House said: “The President said very strongly in his statement yesterday that he condemns all forms of violence, bigotry and hatred and of course that includes white Supremacists, KKK, neo-nazi and all extremist groups.”