One of the easiest bets is the Stockholm Archipelago. Thousands of beautiful islands to pick from and plenty ferries to reach them (or better still, get your own boat).

The Isles of Scilly are rather lovely, although not the most accessible via *A (there are DUS-NQY flights in the summer, otherwise you're looking at BRU-BRS or the train from London to Penzance).

I have friends who swear by the Ile de Batz every year (I've yet to go). You need to get to Brittany first, of course (train from Paris?)

Sark is a fascinating place (accessible via JER, which does have some seasonal *A flights, or more easily from GCI).