If you plan fare enough ahead several airlines do ANC/LHR this week for $910 round trip though it involves a long layover in Seattle.  But ONLY in Seattle.  The British tax rules seem to suggest it would be cheaper to fly into Gatwick or Manchester but the airlines seem more interested in building their Heathrow traffic so that's where the best prices take you. Once in London, use the tube to central London - cheap, especially if you guy a "Visitor Oyster Card" online.  Older hotels, clean but outdated, are amazingly inexpensive.  Good to buy some British currency ahead so you don't have to delay once in London.  Once there, get cash from ATM machines, many charge no fee, at the most favorable exchange rates.  Just be sure you have enough balance in the account you'll draw upon.  Beyond London, great things to see all around the country and rail service, tickets bought online about 12-weeks in advance with Senior Rail Cards (65+) cheap and good when not on strike.