Foreign Secretary William Hague called for restraint in crisis-hit Ivory Coast as a charity said many of those fleeing the violence were children.
Fighters loyal to internationally-recognised president Alassane Ouattara have been battling for control of the presidential palace in the capital Abidjan, with forces still loyal to incumbent Laurent Gbagbo.
Charity Save the Children, which is running refugee camps in neighbouring Liberia, said the majority of those fleeing were children.
The United Nations estimates more than 430 people have been killed in the clashes so far, but aid agencies say the true figure could be higher than 1,000.
Mr Hague said last night: "I am gravely concerned by the violence in Cote d'Ivoire and deplore reports of loss of life.
"I call on all sides to exercise restraint, and condemn the looting and lawlessness reported in Abidjan.
"I am determined that all alleged human rights abuses in the city and elsewhere in Cote d'Ivoire must be investigated and those responsible held to account.
"Laurent Gbagbo must heed the calls from the international community and step down at once to prevent further bloodshed.
"I will be discussing the crisis with (African Union) chairperson Jean Ping during his visit to London on Monday."
Save the Children said 100 children a day were arriving at Bahn refugee camp in Nimba county, Liberia.
Mike Sunderland, a spokesman for the charity at the camp, said: "I spoke to two sisters aged eight and 10 who were walking to Liberia with their mother when gunfire sent everyone scattering. The girls got separated from their mother and lost in the crowds.
"With no-one to guide them, having lost the one person they needed most, they continued their journey on foot for two days, sleeping outside in dark forests and walking in searing heat with no food, no shoes and inadequate clothing."
The charity has evacuated three international staff from Abidjan as security in the capital deteriorates but still has local staff in the area and international aid workers further north. An appeal to raise £25 million for humanitarian work has been launched.
The Government has pledged £8 million for humanitarian agencies in the Ivory Coast and a further £8 million for neighbouring Liberia.
International Development Secretary Andrew Mitchell told the BBC's The World This Weekend the situation in the country had "deteriorated sharply" since Britain sent aid 10 days ago.
He said: "There may now be up to one million people who are on the move going across the border into Liberia, that's why Britain has sent support in terms of food and basic shelter for 15,000 refugees.
"(It's) why we are working to ensure there is water and improve sanitation for 5,000 people who live on the border villages who are obviously trying to help with this weight of people coming through and why, in particular, we have given strong support to Unicef to support the children who have been ... separated from their families on the border."
He said President Gbagbo should go and a political solution be found, adding that like in Libya the international community was intervening with the United Nations and France providing troops on the ground.
He said it was important the situation in Ivory Coast was not "eclipsed" by what is happening in Libya.
Speaking on the BBC's Andrew Marr show, Mr Hague added Britain had been working at the EU and the United Nations to "tighten the sanctions" on the president.
He said: "It's a different case from Libya where the Arab League called on the world, called on the United Nations to become involved and to save civilians from being attacked by the Gaddafi regime. In Cote d'Ivoire it's very much the mood of the African nations that they should be in the lead."