Thanks all for the really helpful responses!

In terms of hotel choices, I think I have now narrowed it down to either Carlisle Bay, Cap Juluca or Malliouhana. The former is obviously Antigua, and the latter two Anguilla.

My OH and I are both foodies, so the appeal of great food, in addition to lovely beaches, is an easy win for Anguilla! However, reaching Anguilla seems to be challenging from the UK - I appreciate you fly to SXM, but doing so from London isn't easy. Antigua on the other hand, is a direct flight (albeit on a shtummer BA aircraft).

I looked at Barbados, and indeed at the Boucan Hotel (albeit as a hotel not restaurant). I felt Barbados was a bit 'done'. I like places which people don't necessarily immediately think of, hence Anguilla and to a lesser degree, Antigua.

I'll spend today looking into the best routings, and then decide between the two islands and hotels.

Massive thanks to vuittonsofstyle, Epicura, Pausanias, worldspan, KatW, katesy, Lovethecabin, AA_ORDlady, erik123 and quitecontrary for all the suggestions and tips!