The warning from the RCGP chair came as a GPonline poll found just one in four GPs were confident their practice would have enough doses of flu vaccine to meet demand - even before rollout begins to patients offered jabs by the NHS for the first time this year, such as patients aged 50-64.
Of 403 GPs responding, 25% expected to have enough stock. Among the 139 GP partners who responded this rose to 27% - but around two thirds of partners also said demand for flu jabs so far this season had been higher than usual, and that they expected their practice to hit or exceed the 75% uptake target for eligible patients.
Professor Martin Marshall's warning over flu jab supplies also follows an announcement last week from high street pharmacy chain Boots that it had paused 'any new bookings for our private and NHS under-65s flu vaccination services'. It said the move was necessary 'due to the level of demand and limited stock that we have available'.
The government, however has insisted that there is 'no national shortage of the flu vaccine' - pointing out that deliveries of flu vaccinations are always in stages and insisting that vaccination will be available for 30m people this winter.
Speaking on Sky News on 29 September, Professor Marshall said: 'This is a significant problem. There does seem to be greater demand than there are supplies. The issue here is we order our flu vaccines at least six months in advance and we put in our orders before the COVID crisis was recognised.'
The RCGP chair said general practice was prioritising 'those in greatest need', with over-65s, pregnant women, young children and patients with long-term health conditions first in line.
There were currently simply not enough doses of vaccine available to cover the more than 30m patients the government hopes to vaccinate this year, he said.
'The manufacturers are trying to produce more, it does look like they are going to do so, but it does mean that those in the younger groups of people who perhaps are at lower risk are going to have to wait longer for their vaccines,' Professor Marshall said.
He urged patients in lower-risk groups to 'hold tight for now' - adding that enough doses to vaccinate them would eventually become available 'hopefully before Christmas'.
The government confirmed last month that practices would receive an unchanged £10.06 fee per flu vaccine for the 2020 campaign in an updated specification for the flu DES.
Health secretary Matt Hancock promised in March that more than 30m people would be vaccinated this year in the 'biggest flu vaccination programme in history'.
However, the DES provides little detail on plans for the expanded cohort - and makes clear the government will only press ahead with the expanded campaign once other groups have been vaccinated, subject to vaccine supplies.
The DES says: 'The programme may be further extended in November and December to include those in the 50-64 year old age group subject to vaccine supply and after existing eligible groups have been prioritised.'
Plans to roll out jabs to this group will be announced 'later in the flu season', with rollout to each additional year group to be considered and announced separately.
One GP responding to the GPonline poll said the flu campaign was a 'complete farce'.
The GP said: 'Having the government announce all over-50s will be eligible at literally the last minute, yet not stating clearly that they will not be vaccinated until November or December IF there are stocks left means we will be spending time fending off requests for vaccination by the "worried well" for September and October.
'When it all goes wrong - ie there are not enough vaccinations to give them to everyone it will be blamed on GPs not ordering enough rather than the government getting it completely wrong...again.'
A DHSC spokesperson said: 'There is no national shortage of the flu vaccine, with enough doses for 30m people to be vaccinated in England. It is completely wrong to suggest otherwise.
'The vaccine is already being delivered for those in at-risk groups, including the over-65s and this will continue throughout the winter months, so there is still time for those eligible people to get their vaccinations.'