The Secretary of State for Defence, George Robertson, warned, however, that many thousands of Kosovar men remain unaccounted for. "We've had several hundred men cross the border from Kosovo. That could leave as many as 200,000 other men of military age who are missing," he said.
The warning came as a United Nations investigator said he had signs of huge-scale ethnic cleansing inside Kosovo. "It is pretty revolting," Sergio Vieira de Mello told reporters after a three day trip to the province.
In Macedonia, tension is mounting dangerously under the twin pressures of the refugee influx and the prospect of huge numbers of Nato troops arriving. An unwilling partner of the West in the confrontation with Slobodan Milosevic, the atmosphere in Macedonia, with its large Slav majority, gets more fraught by the day.
A clear sign of this came yesterday when Macedonian border guards facing the arrival of more than 20,000 refugees in three days tried to head off a stream of them towards Albania. Chaotic scenes followed when buses being driven towards the Albanian frontier were stopped by a UN vehicle.
After hours of increasingly heated exchanges, during which UN refugee agency officials accused the Macedonians of breaking international agreements and their promise last week to the UN secretary-general, Kofi Annan, not to move the refugees forcibly, they were eventually allowed in, albeit at a painfully slow rate.
Both Nato and the UNHCR are puzzled as to why so many refugees have once again begun to appear at the border. Ron Redmond the agency's spokesman said: "All we do know is that it is on a very large scale and very, very organised. Who knows why this is happening now? Maybe the aim is to add more and more pressure on Macedonia."
If that is the aim of the Milosevic regime, then it is having some success. Since the US embassy in Skopje was attacked by rioters in response to Nato air strikes, the atmosphere has been uneasy. Now, with the knowledge that their country is about to become the launch-pad for a possible ground- troops intervention, the mood is turning sour.
Most Macedonians are openly sympathetic to Serbia. There have been a number of attacks on Nato properties and confrontations with troops. The Prime Minister, Ljubco Georgievski, has admitted that "the two biggest problems the country is facing are the inflow of refugees and the emergence of anti-Nato and anti-American feelings among the public".
His coalition government has not managed to control either of these. In charge of a stagnant economy with staggering unemployment figures, the government is increasingly seen by the public as unable to stand up to Nato's demands on troop deployment, and as having failed to extract economic advantages in return.
Most Macedonians believe that as a country of just 2.2 million taking in more than 230,000 outsiders they should be the recipients of much more economic help from the West.
Lucija Popvska, senior official with the Macedonian Centre for International Co-operation, the country's main think-tank on politics and development, said: "These are my personal views. But there is a widespread feeling that the government is being bullied by Nato and others and seem to do nothing about it.
"There have been all kinds of figures about how much aid this country was going to get from the West, but where is it?"