On 1 February new arrangements for England and Wales meant GPs could send oxygen requests for patients directly to suppliers.
Previously, GPs prescribed oxygen on a standard FP10 for pharmacies to provide cylinders through a local gas supplier.
A spokesman for Air Products, which supplies Wales and much of England including the North West, Midlands, Yorkshire and the South West, said it had been inundated with GP requests.
The demand has been so large that many GPs have been unable to fax through their home oxygen forms or get through on the telephone.
Dr Ian Whyte, a GP in Whalley, Lancashire, sourced oxygen from a local pharmacy when an order placed on behalf of a lung cancer patient receiving palliative care was not met.
'The pharmacist still had some cylinders, but the patient died soon afterwards,' he said.
GPC member Dr Trefor Roscoe said: 'I heard that one patient had to be admitted to hospital to receive oxygen. Suppliers had months to prepare for this and should have been ready.'
Air Products has blamed overwhelming demand.
A spokesman for Air Products said: 'We expected 250 calls a day and could handle 1,000 but we received 6,000 calls and a huge number of faxes.' The company received over 2,500 faxes on the service's first day.
The DoH said GPs should remember FP10s can be written until the end of March and will be valid until the end of July.
'If GPs are concerned about delays to their patients' oxygen, they should arrange with local pharmacies to continue to provide this service,' said a DoH spokeswoman.