Absolutely. As previously mentioned, we might expand to deny NHS services to people climbing rocks, riding bikes, playing sport. We could even go down the rabbit hole of limiting access to people that smoke, vape, drink, eat fast food, sugar....
The problem here is that people have become used to knee-jerk, poorly thought through reactions. It might seem to some to be logical to effectively force the vaccine onto people by denying healthcare access, but it would have serious consequences that could not only impact the health on different demographic groups, but would likely create a two-tier society (think the original Demolition Man). It should have been obvious from the approach taken by the government last year that trying to scare people into consider options is not the way to go.
We need to remain civilised, and democratic with this. The vaccine is optional, and the only way to help people make a decision to have it is to have a adult conversation, discuss the pros and cons, and let people make their own risk assessments. As we have seen in this country, most people will opt to have it. There is no need for a re-emergence of "Project Fear" to coerce people into compliance. We are approaching the point we can, and should stop pressuring society.