Officials say there have been no specific threats to British diplomats, but about half of the staff working in Kyiv will return to the UK.
The US has ordered relatives of its embassy staff to leave, saying an invasion could come “at any time”.
Russia has denied plans for military action, but tens of thousands of troops have amassed on the border.
The embassy moves were described as precautionary, and nothing specific is thought to have occurred in the past 24 hours to have triggered the decisions of the US and UK.
EU staff in Ukraine will stay in place for now, with EU foreign policy chief Josep Borrell saying he would not “dramatize” the tensions.
Members of the Nato alliance, including Denmark, Spain, Bulgaria, and the Netherlands, are sending more fighter jets and warships to Eastern Europe to bolster defenses in the region.
With an estimated 100,000 Russian troops now at the border with Ukraine, the head of Nato has warned there is a risk of fresh conflict in Europe.
The US also told non-essential staff they could leave Ukraine, stressing its moves were not an evacuation. But the State Department news agency that if there was a Russian invasion, it would “not be in a position to evacuate US citizens”.
Americans have also been warned by officials not to travel to Ukraine and Russia due to the “potential for harassment” against them.
Ukraine said it was “premature” of the US to withdraw relatives of staff, calling the decision “a display of excessive caution”.
SOURCE: NEWS AGENCIES