Yes, some air rifles are legal in the UK. However there are strictly enforced limits on the power of even the air rifles. It really is pretty low so that what is considered the low end rifle in the US is just barely legal in the UK. The rig described is simply a modest small game/squirrel/garden pest eliminator.
What does it say about an "ally" that hands out 16 year jail sentences for the same kind of rig we train kids half that age on?