Pharmacists and GP surgeries are having to limit flu jabs to the most at-risk groups due to increased demand.
The Boots chain has suspended its appointment booking system for anyone outside of the vulnerable groups, which include people aged over 65.
It said it faces "unprecedented demand" for vaccinations, but NHS England says enough stocks are available.
This year, up to 30 million people can be vaccinated in England, the government says.
Vaccines are delivered in batches to pharmacies and GPs so priority is given to the most at-risk groups.
Within the next few weeks it is likely that winter flu will start to circulate alongside the coronavirus.
This will potentially present an additional challenge to an already stretched healthcare system.
This year in England, Wales and Northern Ireland, for the first time the flu vaccine will be offered to the over-50s - over-55s in Scotland.
But this will only be after it has been given to those who normally get a free NHS jab - including the over-65s, pregnant women, and people with conditions like lung disease or diabetes.
This year, the free vaccination is being offered in England to:
- Adults aged 65 and over
- People with some medical conditions, including diabetes, heart failure and asthma
- People who were required to shield from coronavirus - and anyone they live with
- Pregnant women
- Children aged from two to 11
- Health and social care workers
The NHS offers the flu vaccine via your GP or your local pharmacy.
In a statement, Boots said: "This year, our customers have been more conscious than ever about protecting the health of themselves and their families, and protecting against flu has been front-of-mind for many of us.
"As a result, we have seen more people than ever booking early to get their flu vaccinations."
A spokesperson for the Department of Health and Social Care said: "Delivery of flu vaccinations is phased over the autumn and into winter, and priority is rightly given to those who are most at-risk with others being asked to wait to later in the year."
Deliveries of flu vaccines for at-risk groups will continue in all areas in England throughout the winter months.
Pressure on stocks
The Royal Pharmaceutical Society (RPS) says other independent pharmacies have also had to slow down the rate of vaccination.
Robbie Turner, RPS Director of Pharmacy, said: "This year many more people are anticipating receiving a flu vaccination and they need assurance that sufficient stocks are available.
"We will continue to talk with government on the supply of vaccines, and how pharmacists can support those who are most at risk."
Professor Martin Marshall, Chair of the Royal College of GPs, said widespread flu vaccination would play a key role in preventing the NHS being overwhelmed this winter.
He said the government must ensure there is "an adequate supply of vaccines for everyone who wants one" among patients now eligible and called for guidance on who should be prioritised for the flu jab if supplies are limited.
Supplying the vaccine - which needs to be refrigerated - is a logistical challenge. But NHS England says there are adequate stocks in place.
The Department of Health and Social Care says it will issue guidance shortly on how pharmacists and GPs can access additional stockpiles if needed.
It is unclear how bad flu might be this winter - some years are worse than others - but experts say the vaccine is a good match for the strain of flu that will be circulating.
Flu, like coronavirus, is a viral infection that is passed on through coughs and sneezes. Social distancing, masks and handwashing should help reduce the spread of both.
Most people with flu recover at home in a week, but people with chronic conditions or who are over 65 should call NHS 111.
If you think you have either flu or Covid-19, stay at home and self-isolate.
Book a coronavirus test if you have:
- a high fever
- a new, continuous cough
- a loss of, or a change to, your sense of smell or taste