Don't know if this will help, but if you have smart phone or tablet, people should download the NHS app... This is different from the NHS covid 19 track and trace app. The NHS app once installed on your device will contain not only your jab details, but also your medical records, prescriptions and the ability to reorder. So useful, not only when in the UK, but could be invaluable when abroad.
Absolute cazillions of cash has been thrown at the NHS to produce this, yet its never promoted and so few know of it.... and that includes Dr's receptionists! Greece will admit you in, providing you have proof of having 2 jabs at least 14 before flying in, and the NHS app will provide that.
Also, as at today, when returning to the UK, you have to have purchased in advance your day 2 and day 8 PCR test kit's. I am flying in next week with Ryanair, and they have an arrangement with a pharmaceutical company called Randox, whereby these can be bought in advance at a discounted rate. Mine cost me £120 for the 2 and they arrived within 24 hours. These PCR kits all have a unique ref number which I believe you have to include on your UK PLF which you have to complete before you fly home, so if you are an independent traveller, plan ahead.
I think most airlines or tour companies will offer these to travellers at discounted rates as its a mandatory requirement for people returning to the UK.
Fingers crossed at the next review, Greece gets on the green list, so only a day 2 PCR is required. Hope this helps, but a reminder to get the NHS app installed... Jon Bell