There are options to get a family of 5 from SEA to LHR in Main throught the summer. As mentioned, AA156 has oodles of space. Selecting an arbitrary date of July 11th, there are at least 7 seats in Main. 30K miles & $19 per passenger. The flight time is generally sub 9 hours and since May 26th, sans two days, has arrived early, generally about 30 minutes.
5 passengers SEA-LHR

Alternatively, you can purchase the flight one-way for $919, about ½ the return fare for a 10-day to two-week vacation. The flight is Marketed by AS, earns 100% EQM and is $96 cheaper than AA.

If you are looking for business class and willing to pay the BA vig, there is a mixed-cabin itinerary SEA-DEN-LHR on July 3rd. The mixed cabin is AS F connecting to BA J. It will set you back 325,000 miles and $4,446.00 for 5.
The other airline not mentioned is AY. You can fly Finnair SEA-LHR for 30K miles in Main with or without a stopover in Helsinki, without breaking the piggy bank. A little bit more difficult to find 5 awards on one flight from SEA. If September is workable, you can fly SEA-DFW-HEL//HEL-LHR for 30K AS miles & $36.50. There may be other dates earlier via LAX, JFK, ORD and DFW but there is no availability on any AS flight to those gateways. I didn't search beyond a SEA origin.

James