SEA-LHR on BA costs $265 + $450 return in service charges/taxes. OUCH. As guv1976 mentioned, you sort of need to get creative to avoid those surcharges.

I did a quick search for alternatives, and it appears you can fly from SEA-LAX on Alaska, and then LAX-LHR on American and taxes are only $19 + $209 return. Not perfect, but saving over $500 on the other option - but now costing more Avios, and an added connection. Trade-off!

Surprisingly, the YVR-LHR seems to be the best bet - $178 + $315 return in fees/taxes.

Whichever option you choose, you are likely better off to take the ferrry to SEA or YVR to avoid using more Avios for such a short flight (unless you have AirMiles or Aeroplan and can get a short haul award ticket).

Good luck and happy travels!