Last time i was in London I opened an HSBC premier account and get 5.75 on checking and 6.75 on savings. All calculated daily and paid monthly. It’s in GBP, not USD, so I’ve made an extra 2% due to the dollar’s decline since I opened it. I can transfer money for free on the net to my local HSBC dollar account whenever I need it. I believe you can set all this up by phone/fax too.
Highly recommended as HSBC is the largest bank in the world, if they fail we have a lot more to worry about than our savings.