Fahim Manji, who arrived in Britain from Dar es Salaam, Tanzania, on 13 June, is being treated for acute lymphoblastic leukaemia at the Royal Free Hospital, in London.
Dr Michael Potter, consultant haematologist at the Royal Free, said: "The problem the family have got is that without adequate treatment there is a high chance that their son will die. With adequate treatment he has a 60-70 per cent chance."
He has had two courses of chemotherapy and although the disease is now in remission doctors say he needs further intensive treatment to save his life.
His parents, Amin, 36, and Nasim, 38, who run a salt mine in Tanzania, decided to bring their son to the UK when they were told the treatment he needed could not be provided at home. They hastily mortgaged their house in Dar es Salaam to raise pounds 10,000, believing it would be more than enough to pay for his treatment.
When the family arrived at the Royal Free, doctors found that Fahim had malaria and was suffering from kidney problems in addition to his leukaemia. They agreed to treat him on compassionate grounds but warned the family that he would need two years treatment costing between pounds 60,000 and pounds 100,000.
"Fahim is not a British citizen so he is not eligible for free treatment on the NHS," Dr Potter said. "It has to be done on a paying basis. You cannot blame the parents, they thought they were arriving with a fortune, but pounds 10,000 is really a drop in the ocean.
"When the family arrived Fahim was in a mess and we agreed to start treatment even though the deposit they had was not as great as the hospital would have liked. Now they have run up large debts and the NHS is losing money. The hospital wants to be sensitive but it is in a very difficult position. It has been a time of great anxiety for the parents."
The family are staying with relatives in Harrow, Middlesex, and the local newspaper, the Harrow Observer, has launched an appeal for them, chaired by the local mayor. Fahim's mother, Nasim, said yesterday: "We had to do something. It is terrible. I wish I could wake up from this awful nightmare. I never thought it would happen to us."
She said her son was doing well but was missing his friends and felt isolated. "He is very quiet. He understands what is going on and that everyone is trying to help him but he keeps a lot inside himself.
"He cannot go out in public because of the risk of infection. I bought a football for him but there is nobody for him to play with. He is alone."
She said doctors had suggested they return to Tanzania and continue treatment there. "But what is the use if he gets an infection? It would be like signing a death warrant. It is not easy for parents. I would never forgive myself if something happened to him."
In a statement last night, the Royal Free NHS trust said the bill for treatment so far exceeded pounds 35,000 but the hospital had agreed to provide it "as a matter of goodwill and good clinical practice". It said doctors would liaise with medical staff in Tanzania about Fahim's future care.
Donations may be sent to the Fahim Manji Appeal, c/o Harrow Observer, 326 Station Road, Harrow, Middlesex, HA1 2DR.