Not particularly to the UK, but I've had a couple experiences. Domestically, I was allowed to take my SG w/case on the plane and they strapped it onto the seat next to me (the plane was not full). But on the return trip they made me check it and the guitar was damaged (the case was not a true hardshell). This was several years ago. I brought a classical back from Spain in a lightweight case to the US and it was a situation similar to Blues-core, I was probably supposed to check it but I had it strapped to my back and slipped in along with the crowd. I then had to wait until the plane was settleds and the flight attenadnt placed it in the first class storage closet. A bit of a gamble to try to bring it on, since recently (post 9/11) bags are watched more closely.
If you know what kind of guitar you're going to buy you could check and empty case on your way over here, and try to get it on board on the return...if you can't it will protected in the cargo area.
All the best with your trip and guitar hunt.