I suspect that there'll be a system where if you want proof of vaccination your GP will be able to provide same either digitally or in hard copy - for a fee. Easy money for the GP, highly inconvenient for the travelling punter. And of course it may not just be foreign travel that requires proof of vaccination, given the litigious nature of the UK, would you as a large restaurant or cinema chain take the risk of your insurance premiums rocketing because you haven't taken adequate steps to protect customers from infection? There is a precedent for this, PAT testing, which contrary to what people think is neither a regulation from the EU, nor from the UK government but a requirement of insurers to validate business insurance.
Reading stuff this morning, I really can't see much international leisure travel happening before this Autumn; to be honest I can't see much in the way of holidays happening domestically before the school summer holidays either. I feel really sorry for the millions who don't have a back garden to relax in.