Dr Charles Simenoff, a Manchester GP, said: "We normally vaccinate between 400 and 500 patients each year against flu.
One of the companies producing the vaccine says it could be a month before they have completed their deliveries to GP surgeries.
And some GPs, who have had to cancel flu vaccination sessions, say it may be difficult to get elderly patients immunised in time.
The situation appears to be particularly bad in the north west of England, with many GPs having already run out of vaccine.
Dr Charles Simenoff, a Manchester GP, said: "We normally vaccinate between 400 and 500 patients each year against flu.
"We have had to cancel sessions affecting around 200 of them. It's going to be a close thing whether we get everyone done in time. It could cause havoc."
Cooper campaign
He said that the government's flu vaccination advertisement campaign featuring former boxer Sir Henry Cooper had been a victim of its own success.
This, coupled with a particularly virulent flu season last time around, has produced extra demand for jabs.
The flu vaccine is different each year, as separate strains of flu virus emerge each year. So people who need a vaccine must have a new one every 12 months.
The problem this time around is that one company, Solvay Pharmaceuticals, has had problems growing one particular strain of virus to go in the vaccine.
The problem may have been compounded by a late surge in demand for the vaccine caused by a drop in the age threshold for free flu jabs announced by the government in April.
Most GPs order their vaccine supplies a year in advance.
But he said that provided patients received their jabs by the end of November, they were unlikely to fall prey to flu.
He said: "There is no need to panic. If the company cannot supply enough vaccine, I am sure that the other firms will be able to make up the shortfall in time."
The government has introduced a number of measures to try to avoid a repeat of last year's flu-related problems in the NHS.
These include extra money for intensive care beds and to ease the discharge of elderly patients into nursing homes to recover.
Last year's outbreak, although not classed as an epidemic, involved a particularly aggressive strain.
A combination of large numbers of elderly patients and staff sickness placed the NHS under enormous pressure.
Around six million flu jabs were available last year, but only given to about half the patients at high risk.
The World Health Organisation condemned the UK's winter preparations as "inadequate".
A spokesman for the Department of Health said: "The Government's flu vaccination campaign is on course to reach the target to immunise at least 60 per cent of the population aged 65 and over together with other 'at risk' groups."
"Eleven million doses are being supplied by manufacturers to GPs.
"This is four million more doses than last year and more than enough to reach the target population."