Every primary school child in England is to be offered vaccination against winter flu in an attempt to safeguard them and their family from the virus, the health service has announced, promising no shortage of vaccines regardless of the Brexit outcome.

This year’s flu vaccination campaign will be the biggest ever, with 25 million people offered vaccines free, including 600,000 school children aged 10-11. Children are considered “super-spreaders”, liable to infect others in their family and a danger to the elderly. All children aged two to 11 will be offered the nasal spray vaccine in the coming weeks.

Public Health England, NHS England and the Department of Health and Social Care said last year’s flu season was not the most severe, but it still had an impact on hospital and intensive care unit admissions and there were nearly 1,700 deaths.

Those at highest risk are the elderly and those with health problems. Last year 72% of over-5s were vaccinated, a figure they hope will reach 75% this year, said Prof Yvonne Doyle, the medical director at Public Health England. “Every winter there is always the threat of a bad flu season. Flu is a serious illness and can even be deadly for the most vulnerable of our population,” she said.

The uptake among those under 65 but vulnerable because of chronic conditions was 48%, she said, which they hoped to see rise to 55%. Among pregnant women, it was 45%; among healthcare workers, it was 70%. “That has improved remarkably,” she added.

There is a big variation in the rates of healthcare workers being immunised from one NHS trust to another. Some trusts do well, with 90% vaccinated, while others only manage 40% to 50%. Sally Davies, then the chief medical officer for England, told a parliamentary committee in June that all healthcare workers who refused the jab should wear a lapel badge to warn their patients they were not protected.

“The NHS is setting in place a buddy system so the good trusts can teach and partner with ones that don’t have good figures to bring them up as fast as possible,” said Prof Jonathan Van-Tam, the deputy chief medical officer for England.

He said there was an element of professional responsibility about the decision for healthcare staff to be vaccinated. “We do know that flu infections can also be asymptomatic and staff can spread flu without realising it. A patient doesn’t want to think seven out of 10 healthcare workers you will meet will be vaccinated. You want nine out of 10 to be vaccinated,” he said.

Unison, representing healthcare workers, said staff responded best to encouragement. “No NHS worker would ever willingly put patients or colleagues at risk. But the highest vaccination rates are in trusts that encourage staff to get the jab, not those where employees are coerced,” said the union’s head of health, Sara Gorton.

“Pressuring staff to have the injection, when some may be reluctant for genuine reasons, is counterproductive. The NHS couldn’t get by without the goodwill of its staff and trusts shouldn’t jeopardise that.”

Van-Tam said there would be no shortage of vaccines, even if the UK crashes out of Europe without a deal. “There is no possibility that we won’t have enough vaccines,” he said. “This has been very carefully thought through.”

Most of the vaccines needed will arrive in the UK before 31 October, he said. The only exception would be supplies for those under 65 at risk because of chronic conditions. The vaccine manufacturer Sanofi Pasteur would deliver two-thirds of what is needed before the Brexit date, but the final third in November.

The health secretary, Matt Hancock, has ordered an additional 400,000 doses of the quadrivalent vaccine (against four strains of flu) for this group, which would arrive before the end of the month. “We do recognise that it is an extraordinary year,” said Van-Tam.