I had my first swimming Adder just the other week.
Don't worry too much about where you tread,they'll be trying to get out of your way before they'd try a strike.
Was it definitely an Adder? I'd guess it was more likely a Grass Snake.
I'm just making a judgement from the habitat and you saying that it was the first ever snake you've seen but I could be wrong though, not knocking you or anything.
It was Black in colour with a lighter pattern up its back,,the island is only 5m from the shore and 15m across,looked like something had been eating some eggs in a nest ,shells were left l dunno if that makes any diference though.
Wasnt an eel caught enough of them,looking at the pic of the Grass snake 75% sure it was one,thanks again saw my 1st Lizard as well couple months ago didnt even know we had them here.
All snakes are able to swim as far as I know.