The Foreign Office has strongly advised all British nationals to leave Yemen immediately as fighting there worsens.
It said its ability to provide consular assistance was limited, and airports and routes in and out of Sanaa and other cities might be closed.
President Ali Abdullah Saleh has again said he will not step down, despite mounting protests.
Some 72 people are thought to have died in three days of clashes between tribal fighters and government troops.
The Foreign Office is also continuing to advise against all travel to Yemen.
'Appalling' life loss
President Ali Abdullah Saleh has repeatedly said he will not step down and has so far refused to sign a transition deal that would see him resign in favour of a unity government.
Foreign Secretary William Hague said he was "appalled" by the loss of lives and condemned the violence.
He said it would become "very difficult" for the UK to organise the evacuation of any Britons caught up in the violence if it spread.
Speaking after the escalating situation was discussed by Cobra, the government's emergency committee, the foreign secretary said: "We urgently reiterate the United Kingdom's call to President Saleh to sign the agreement, allowing for a peaceful transition and preventing further bloodshed.
"It is now apparent that, should violence in Yemen become more widespread, it would be extremely difficult for the British government to assist its nationals in Yemen in reaching safety."
Mr Hague repeated his "clear advice" that "British nationals should not remain there and instead should leave Yemen immediately while commercial flights are still operating".
The Foreign Office has urged British nationals to remain in regular contact with the Foreign and Commonwealth Office and register with the Embassy by emailing email@example.com.
Those that require consular assistance should call +44 (0)20 7008 1500, it added.
The latest clashes in Yemen began on Monday after forces loyal to President Saleh moved against the compound of Sheikh Sadiq al-Ahmar, leader of the Hashid tribe.
Medical sources told the BBC that 54 people - including Ahmar supporters, women and children - had died in fierce fighting, as well as 18 government soldiers.
More than 250 people have reportedly been injured.