"You must have been fully vaccinated under one of the following programmes:
UK vaccination programme, approved by the Medicines and Healthcare products Regulatory Agency (MHRA)
UK vaccine programme overseas, approved by the MHRA
an approved vaccination programme in Europe or the USA – not all are recognised in England"
That's what it says in the document I quoted originally. You may not agree with it, I don't, but no amount of "checking" will change that. Just for info "UK vaccine overseas" means British Overseas territories, the Channel Islands and Isle of Man, and, of course, crown servants based overseas. So our own dear British Embassy staff, who may have had Astra Zeneca jabs here, can waltz in with no restrictions while you and I must suck it up, because we're second class citizens.