Having said that, Covid-19 vaccines is a positive for the smooth running of the league, vaccines will to a large extent protect many players from contracting the virus, thus the league will go on without any stoppage/break, but the good thing is that if majority of the players get vaccinated, then it'll more or less keep the league going, since it's not compulsory, and it's a personal decision, clubs can try to persuade their players to get vaccinated and I'm pretty sure the majority will, the minority that would not will be more or less inconsequential.
The government control if the Premier League is halted because of Covid. I think in the UK cases are rising once again to the same levels that they were when they postponed the league last time. Vaccines only work to stop spread a little it does not stop it completely and while the pandemic is still going on the Premier League could always be postponed again. UK are doing vaccine passports to enter large stadiums and the same will apply for players I think if they want to play football they will be required to get the vaccine. I think most have already been vaccinated.