Yes, the squirrel fight club is now open in England. Although somewhat hybridized, these are two young female European Red Squirrels, and they often engage in "play fighting", but the acrobatics are interesting nonetheless. Around here, we see similar events among our Douglas squirrels. The general assumption tends to be that males are fighting for dominance and territory. That's not usually the case; they're more than likely female nest-mates.
As you can see - these rodents have no nuts.