The warning from Dr Hamish Meldrum, deputy chairman of the British Medical Association GPs' committee, comes as British scientists heralded a potential breakthrough with a new asthma vaccine.
He spoke out after the BMA revealed that Britain faced a "scandalous" shortage of vaccines and blamed the Department of Health for sending people to their doctor for immunisation, but failing to ensure that GPs had the vaccines needed.
There are shortages of the BCG vaccine against tuberculosis; vaccines against diphtheria, tetanus and whooping cough for infants; diphtheria and tetanus jabs given to children starting school; and the meningitis C vaccine for students starting university.
Dr Meldrum told the Independent on Sunday: "In these cases demand has simply outstripped supply. This raises questions over whether the NHS will have the resources to meet demand in future."
He added: "At the same time as there is potential good news, as scientists announce a breakthrough in research for a new vaccine, the bad news is, on the ground, family doctors cannot obtain enough supplies of the most basic vaccines, developed 20 or 30 years ago."
The new asthma vaccine offers hope of lifelong protection from a single injection. It would transform the lives of the growing number of sufferers in Britain - 3.4 million people, 1 million of them children.
A team led by Stephen Holgate of Southampton University, found in preliminary trials that the symptoms of patients with mild to moderate asthma were reduced by 30 per cent on average. The vaccine uses dead, soil bacteria from Africa to prime the body's immune system and dampen allergic reactions that cause asthma.
But even if further trials prove the vaccine does works there are no guarantees the NHS will be able to cope with demand.
Doctors across the country have reported a shortage of meningitis C vaccine, which ministers promised would be available to all first-year students. The Department of Health blamed the shortage of diphtheria and tetanus vaccines on the manufacturers - who blamed machinery breakdown. But a spokeswoman assured that supplies of all vaccines would be increased.