"Football needs to wake up," he told Telegraph Sport. "If they can't put a team out I would award the other team a 5-0 victory. You might need to bring it in in a couple of weeks time so they get time to be vaccinated. The football leagues need to get a grip."
Although Prof Neal stressed that some cases among footballers were inevitable, due perhaps to having children in school or partners at work, mass outbreaks and unavailability inside the same club could largely be avoided with sensible mitigation.
A particular problem for clubs with high numbers of unvaccinated players is that they must self-isolate if they are deemed to be a close contact of a positive case regardless of whether they were themselves infected.
"It is possible to contain the spread within the football club environment," said Prof Neal. "When a whole team is getting Covid, the scientific term is that insufficient Covid precautions were being taken.
"You can't keep Covid out of the household - you might have children in school, you might be married to a nurse. And you can still catch it when you are vaccinated. It's when eight players get it. The football clubs should be responsible for that. I just don't get it. They [the players] have a right not to be vaccinated but unvaccinated people do not have a right to go around spreading Covid which may end up with me or my mother catching it."
Dr Gabriel Scally, a visiting professor of public health at the University of Bristol, also agrees that, as in the NFL in America, there should be circumstances whereby individuals clubs are culpable for postponements.
"That would change the [vaccine] situation," he said. Of the 'individual choice' argument, Prof Scally said: "You can't have individual choice in an infectious disease. The hint is in the word 'infectious'. It spreads from person to person. It's not like someone making a choice over whether to have a symptom investigated that might be cancer-related.
"These are clearly professional people whose job involves them coming into close contact with others. It is not just someone putting themselves at risk. They are also putting other people at risk."
Prof Scally said that the first priority should be to understand why there is such hesitancy among English-based footballers.
"These are extraordinarily fit younger people for whom vaccination is likely to pose no problem whatsoever," he said. "Not to try and find out and deal with that is negligent in my view. It is an important issue and has to be sorted out particularly because it is such an extraordinarily bad example to the rest of the population.
"At the moment, decent behaviour includes being vaccinated to save the NHS from having to look after you when it has got other things to do, and also to save your colleagues and others that you might affect."
Prof Neal said that he was "not too worried about the football crowds" in an outdoor environment but described the World Darts Championships that is currently taking place at Alexandra Palace as "Covid-spreading on steroids". He added: "That is risky. You have got enclosed space, people not wearing masks and the behaviour is not conducive to Covid control."