The UK Govt cannot say it publicly, but is almost certainly worried about vaccine paperwork fraud. Even in the UK, I've been offered a "cholera vaccine exemption" yellow book vaccine passport from a UK based doctor in return for money.
Denmark has adopted a policy of recognising vaccines in OECD countries (as well as the EU). Presumably their belief is that rich countries see less vaccine paperwork fraud, because vaccines are widely available and thus fraud becomes unnecessary. If however you claim to have been vaccinated in a poor country...
If the UK and EU can't or don't want to make their vaccine record systems mutually compatible.... perhaps the UK could follow the Danish approach ? Or would an OECD-only approach leads to legal risk around being discriminatory ?