I agree with "the Doc", I have had good experiences with ICICI, they are easy to deal with on-line, they have a secure email connection (when logged on) to which they reply within 24 hours, the staff are polite if you have to call them (naturally they're based in India, but you call a UK number) but my phone experience has always been good.
Whats more their products tend to offer "best buy" rates, particularly the fixed term accounts.
I thoroughly recommend them for your savings.
John