Hey! I also knew how to ride a horse before a bike.
I sold my horse in order to move here, and occasionally have moments of doubt with that. (Not the decision to move, but I do sometimes wish I could've managed to bring him over!)
I've done the "go out and try a lesson" at a few stables, and have found them all to be pretty decent, but fairly tourist-y (this is central London, though, so that's to be expected).
I've been sticking with places that have BHS training, as I figure the instruction level will be pretty good. The BHS (British Horse Society) has approved riding centres/liveries on their website, which is pretty handy.
https://www.bhs.org.uk/I'm hoping to move out of London in a couple of years and take up horsey stuff regularly again - it's too expensive/time-consuming here in London to try to ride a lot (1hr one-way commute to the barn, so weeknights are virtually impossible). I compete(d) in eventing, so this is Mecca for me - I just have to get out of the urban gridlock so I can take advantage!
Re: Arabians, I don't know that I've seen any (mostly Cobs and TBs/RIDs), but I know France is quite into the Anglo-Arab, and obviously Poland's not far away, so I would bet you could get some really nice bloodlines once you went shopping.