In reply to Chris Craggs:
Depends on the airport. When I flew to the UK and back from Lyon, I had hand luggage only and didn't have to show any evidence of jab until the boarding gate. This seemed stupid as a great opportunity to slow things down. I used the Verfly App which stores all your evidence, validates it and gives you a big tick to show to whoever asks.
Coming back from Heathrow, I wasn't able to check in online so was forced to queue for an in-person check-in. That's when I had to show my evidence.
I flew to Amsterdam on the first day of the vaccine passports in France and leaving AMS they didn't check anything but that was an internal Schengen flight - just the automatic departure gate like a Tube turnstile.
Same with Paris->London Eurostar the other day. They were checking vaccine status of everyone in the queue as we were lining up for the checkin gates.
> As I understand it the real checks are when you arrive in your destination
I've not been checked in any destination (although admittedly only Lyon, London or Amsterdam in the last couple of months), just always on departure. Even French border control haven't asked for any of the paperwork on arrival.