We can all calm down a bit - at least if you believe Michael Gove (who, whatever you may think of him, is closer to the throne than Nadhim Zahawi and appears to be BoJo's leaker-in-chief)
www.bbc.co.uk/news/uk-55143484
The plan is not (currently) to offer vaccination passports, because at the very least, it is not yet proven that having been vaccinated prevents you from carrying the virus asymptomatically and passing it on.
If that WAS eventually to be proven..... well, private enterprise will do what it likes. If foreign countries choose to make vaccination mandatory to enter, that's their right - whereas foreign travel is NOT a human right, except in the case of escaping persecution. There are already some forms of employment in which some vaccines are mandatory, such as Hep B for NHS staff.
The government, however, has a duty to ensure all its citizens have access to all the things they need for a decent basic standard of living. It's a shame they don't do a better job of fulfilling that... but, that aside, it's my view that if supermarkets for example tried to demand vaccination passports before entry, the government would prevent them from doing it in a blanket way.
What they could do is have certain time slots which were only for vaccinated people, limiting the hours during which unvaccinated people could shop and requiring e.g mask wearing during those times, whereas the rest of the time masks would no longer be required.
Would that be acceptable, OP? You still have access to what you need, albeit with some limitations. Whereas those who have chosen to be vaccinated have more choice.
Please remember that 94% effective is not 100% effective. Some people who have had the vaccine will still go on to catch Covid, so IMO it is reasonable for them to be able to choose to limit their exposure to unvaccinated people, who are much more likely to be carrying it than unvaccinated ones.