My old bitch got bit by an adder a couple of years ago, I toook her straight to the vet who gave her drugs, can't remember what though and she was OK. This happened in September, seemingly the later on in the season, the more venom the snakes produce. Fortunately I saw her fooot had swelled up and she was looking sorry for herself.
Ever since then, I carry a couple of Piriton tabs in my phone cas just as a precaution. I would find it diffficult to believe that there are adders about at this time of year though. Put this to your vet and see what they say.
Cheers, D.