Hello! As you can see <twirl> I have Obviously Name Changed 
I live here. Welcome! It's a nice friendly village.
Ok, so the weird thing about Dorchester is that it's right on the edge, geographically, of a big baggy catchment area for all the Abingdon secondaries, even though Wallingford School is, what, 8 minutes drive away and clearly the closest both as the crow flies and on the road. Dorchester kids feed into the three Abingdon schools as per catchment. BUT I would say that the majority of the state secondary kids here are at two of the three Didcot state secondaries - they are, somewhat unusually, segregated by sex. St Birinus School is the boys, and there's Didcot Girls' School. They are both very well thought of, and my son is at SBS. He's largely happy there. I know a lot of parents who are very happy with SBS and DGS, a few who found that the (very academically aspirational) atmosphere at DGS was a bit too oppressive and effected a move elsewhere successfully. We are lucky - there are a LOT of good secondaries in this area. 
When we did all the open days, we did look at two out of three of the Abingdon schools and I have to say, I wasn't that convinced. But I do know students at John Mason who are enjoying their time there and doing well. Wallingford School used to be massively oversubscribed and it was pretty much a given that an application from Dorchester wouldn't get in, you'd have to appeal. In the end, we all decided that DS would be happier at SBS anyway. Having said this, that was a few years ago and things have changed. It may well be easier to get into Wallingford as your first choice - but I'd urge you to consider the two Didcot schools (not the third one, Aureus!) I've mentioned here.
DM me if you'd like a chat. (I'm shit at checking my messages on MN but I'll try to remember.)