Some kind of vaccine passport for overseas travel, yes. It makes perfect sense because it gives them confidence that you stand very little chance of being a drain on their local medical resources and are highly unlikely to be spreading something new.
Needing vaccine passports within the UK? Definitely no! - it's almost verging on hysteria now and is pointless and illogical if you think about it. Lots of businesses and venues are now saying they don't want to employ/admit anyone without a passport because "we want to protect our staff and customers". The hugely overwhelming point of having the vaccine is to protect yourself against serious disease or death if you do get infected. Yes, there's a secondary effect of the vax in giving protection to others because of reduced transmission etc but that will be afforded to everyone else equally - those with or without a vaccine - and it's coming from you, not them. Bear with me! If you sit next to an unvaccinated person in the cinema, who is most at risk? They are of course because you've got your safety shield, they haven't. The protection those company bosses spoke of already sits with all those staff and customers who are vaccinated and is helping to protect all the people they mingle with. Yes anyone could still be unlucky enough to catch Covid but the unvaccinated are the ones taking the bigger risk. Substitute the world flu for Covid and you'll appreciate the nonsense that this is. Ultimately, we should hopefully be able to live with Covid as we live with flu - it's out there and it could be deadly but we've had our jabs.
Another point is that our percentages of people taking up the vaccine will likely ensure that case numbers eventually remain very low in the UK. The fewer cases there are in the community, the less chance it has to mutate into something nasty. The small proportion of unvaccinated people are more likely to be infecting each other than those who rolled their sleeves up but there won't be enough of them to effect the whole picture.