The 20 squatters moved into the empty 20-bedroom house opposite the Natural History Museum in Kensington last week.
But they face eviction before Christmas after the owners, the University College London (UCL), began legal action to have them barred from the former student hostel, which is equipped with furniture, shower facilities and television. The university will apply for a possession order in the County Court next week. The property is for sale.
A university spokesman said: "We are entirely sympathetic to the situation faced by the homeless in London but unfortunately the occupation of a property for a short-term period is not the answer."
Organisers of the squat gained entry without causing damage, forcing UCL to resort to civil action rather than criminal proceedings.
The residents said last night that they were acting on a promise given by the Deputy Prime Minister, John Prescott, that the homeless would be housed over the millennium.
Henry Battersby, 37, a Big Issue seller, said: "It's safer and more secure than being on the streets and this place has been empty for quite some time. There are not many vacancies in hostels at the moment, especially at this time of year. All we've done is to try and take John Prescott's policy into our own hands - it's not an answer to homelessness but it's a step forward."
The Department of Environment, Transport and the Regions said Mr Prescott's pledge applied only to the new year.Reuse content