And because I'm Scottish, I've gone through my music collection and can add the following bands as well. 

Big Country, Nazareth, Del Amitri, Texas, Franz Ferdinand, Simple Minds, Eurythmics... I could find more but they're the bands I love. 

Not a rock band strictly speaking but i cannot imagine british musical scene without D.e.p.e.c.h.e M.o.d.e  :)

How about Def leppard. I really love that band 

Pink Floyd, Led Zeppelin, and The Beatles lml

If you´re into contemporary alternative rock I like Alt-J and Glass Animals. And a few years back Mumford and Sons came to my state of Alabama and I had a chance to go. They are truly talented live. It was a great experience.