Staff have been allowed back into part of the Royal Marsden Hospital following a serious fire.
The Prime Minister met patients on Thursday morning
The blaze broke out at the leading cancer treatment centre on Wednesday and destroyed about half of the roof.
A hospital spokesperson reported that the damage to the building was "not as bad as first suspected" and a clean-up operation had started.
Gordon Brown said the government would do everything in its power to fully reopen the site as soon as possible.
Eight fire engines and 50 officers remain at the site, but an administrative centre has been set up in the building to keep patients informed.
Cally Palmer, chief executive of the Royal Marsden NHS Foundation Trust, said: "We are working as quickly as we can to get the Chelsea hospital up and running and our main priority is to ensure continuity of care for our patients.
"We are extremely grateful to all the help given to us by our neighbouring hospitals."
Five operating theatres and two wards were badly affected by the blaze which swept through the building on Wednesday.
Patients will continue to receive their treatment from Royal Marsden specialist teams either at the Royal Brompton or the Royal Marsden's sister site in Sutton.
Prime Minister Gordon Brown visited the Royal Brompton Hospital with his wife Sarah and Health Secretary Alan Johnson.
He described the fire as "one of the biggest emergencies that the health service has ever seen".
Mr Brown said: "The last 24 hours have seen Britain at its best."
He praised staff for saving equipment and added: "We will now do everything in our power to make sure the Royal Marsden can be up and running as quickly as possible.
"The rebuilding work will start immediately."
About 800 staff and up to 160 patients were evacuated during the fire, including two patients undergoing surgery.
Fire investigators are searching for evidence to establish the cause of the fire, which broke out shortly before 1330 GMT on Wednesday.
It is understood investigations will include the area where construction work was taking place.
The fire started on the fourth floor and destroyed much of the roof
Six people in intensive care were among the 79 in-patients moved to other hospitals.
Out-patients were taken to the nearby church of St Paul in Onslow Square before being admitted to other hospitals or allowed to go home.
Chelsea Fire Station crew manager Justin Orrin helped carry an anaesthetised patient from an operating theatre.
He said: "Debris was falling outside the window and we had to take a gentleman out of theatre but the exit we came to wasn't safe so we had to find another route."
He said the man regained consciousness while being carried out of the hospital on a mattress.
The Royal Marsden was the first hospital in the world dedicated to cancer treatment and research, seeing more than 40,000 patients from the UK and abroad every year.