I had HSBC in the states and hated them. They're a huge corporate bank and don't give a d*mn about individual customers of modest means. In the UK I've got Lloyds, for no other reason than that my husband banks there, and they gave me an account with no hassle. I haven't had any problems with them. Their internet banking is pretty convenient, and they've never called me, though they do send me offers in the mail along with my statements. I think if you get a silver account, it has some special setup for sending money internationally to other people, not necessarily to other accounts. I don't know what their international wire transfer rates are, as I've never done one.
I think if I had to set up an account at another UK bank, I'd choose Barclays. They seem to be pretty good.