When I first came over in 2007 I banked with Lloyds. They were fine, but nothing to write home about. When they finally agreed to give me a credit card, the interest rate was ridiculous because - even though I'd been with them for several years - I was new to the UK and a "credit risk."
Two years ago or so we switched to First Direct, and they've been excellent. Friendly and helpful on the phone - which they answer directly without you having to press a thousand buttons to get through automated menus - and happy to give me a credit card with a reasonable rate immediately. Maybe that's because I'd been in the UK for a few years and established credit, but either way they're a better bank overall.
Hope that helps.