It's kind of a shame actually that this sort of thing is uncommon in the UK, since we actually, you know, have the history and historical locations for it.
Closest you can get is a lot of English Heritage/National Trust castles will do their own events and things, where they might show actual archery/knight-combat reenactments.
If towns and villages got into doing them it would be great. Depending on where you are in the country it's not all that difficult to find old castles/forts/ruins either, and there are still lots of thatch-roof cottages and Tudor-style houses around, which would really help with the atmosphere.