From London, cheap excursion fares can be had to Spain on Iberia. You can maybe think of doing a weekend thing.

From Manchester, Cathay Pacific flies between there and Amsterdam or Paris. It has full traffic rights. You can maybe check out with a big travel company in London to see if they can offer you any special fares which you can accrue miles on. On AA, you can currently accrue miles only on fares ticketed in Y, B or H class.