I’d be all for that personally although it is dependent on the level of testing resources available. They do seem to be doing it for hospitals thankfully
Vaccinated people can carry the virus and spread to others but their chances of being infected are still less than an unvaccinated person so requiring vaccinations for indoor will still be somewhat effective at reducing spread and the unvaccinated requiring hospital care assuming the rules are followed.
At each of the three gigs I've been at over the last few weeks (1 at Ally Pally, big 10,000 venue in London, 1 at Manchester Victoria Warehouse (3,000 capacity) and one at O2 Academy in Leeds (2,500)), there was lateral flow testing available on the door for people who didn't have a vaccine pass, immunity pass (180 days) or a negative lateral flow result to show. It was adhered to very strictly at each venue.
There's a hell of a lot to criticise about the UK's covid approach. The testing, to be fair, isn't one of them right now. They are available pretty much on demand, even PCR tests, and for free. They should stay that way for the next six months IMO.