The Royal Marsden is planning to open its outpatients department and its Medical Day Unit on Monday at the Chelsea site.
The Medical Day Unit will be able to dispense chemotherapy, while patients to the Outpatients Department will be able to continue their consultations with clinical teams who have been contacting patients all day by phone and will continue to do so tomorrow.
This follows the clean-up process which began in earnest on Wednesday night.
Cally Palmer, Chief Executive of The Royal Marsden, said: "We are working as quickly as possible to get the Chelsea hospital up and running.
"We have brought in professional contractors to assist our own teams to clean up the hospital and to get our patient areas ready for business again.
"And by the end of next week, we also hope to bring back on stream some of our wards that are unaffected by the fire."
Others who require radiotherapy will have their planning performed at Sutton.
Cally Palmer continued: "Our thanks go to our healthcare partners who are pulling out all the stops to help us. And the help and support we have received from The London Fire Brigade, the London Ambulance Service and The Metropolitan Police has ensured that we are getting back to business as soon as possible. Our heartfelt thanks go to them."