Yes bob is correct. The ones issued on paper and sent to you by the NHS have no end date. The ones you download using the NHS app last for thirty days from the date of download, but you can download them as frequently as you like. The downloaded ones now show all three jabs. I imagine any new paper ones will too, though I haven't checked.
I think bob is also right when he says the UK government has no will to enforce their use for entrance to pubs, shops, etc. I also doubt that the devolved governments will extend their use beyond the current arrangements for nightclubs, large events, etc. (though I believe they are also required for cinemas and theatres in Wales).
The resistance to it is not confined to Tory voters. We don't do "papers" in the UK. People are generally free to move about unhindered for most purposes. You don't even have to carry your driving licence with you when driving. The need to produce proof of having had a non-mandatory medical procedure carried out smacks of a totalitarian regime. That said, nothing surprises me when it has the term "because of Covid" attached, but I'd like to think any UK government would deem this a step too far. Apart from that, there are the practical problems. Hospitality venues have been badly hit by the restrictions of the last 18 months and I doubt they can afford the extra staff required to vet their customers' health status at the door on a busy Saturday night. As far as public transport goes, where I live they cannot even prevent people travelling without tickets so it's hard to see how they would prevent suspected plague carriers from boarding their services.