Rob, and others, I can't guarantee it'll work every time, but if you're looking for tickets from the UK to the US (or anywhere else long haul for that matter) in premium cabins, and have some time when you travel, have a look at booking from mainland Europe, e.g. Frankfurt, Amsterdam, Lisbon, to London to Minneapolis.
You can often get much lower prices on American or BA; Delta sometimes. You have to start in Europe, so you need to get yourself to Frankfurt or Amsterdam, then come back to London. On the return you can build in a stopover in London and ignore the last leg. My last ticket to South America via New York on American, starting in Amsterdam, cost me £2000 when business class from the UK, on the same flights was £3700, and I've managed to pick up a return to Capetown on BA in business later this year for £1400.
Structure it right and you might be able to check-in the guns in London. Similar price advantages often exist for flying from the UK via somewhere else, e.g. on Lufthansa via Frankfurt, KLM via Amsterdam, etc.
