Just a follow up.
The NHS app being off-line could have been why the Ryanair staff today were asking everyone if they had the vaccine and taking their word for it before letting them on the plane. I was surprised at the time but it makes sense now.
Also at Alicante I had to show my NHS letter as well as my locator form - first time I can remember them checking the NHS app/letter.
It seems Ryanair have handled this a lot better than Easyjet.