I had a small # of UA miles expiring a few years ago, and chose a 15,000 mile award on British Midland (now BMI?). When I redeemed it last December, I believe I received a refund of 5,000 miles because the necessary mileage had dropped.
Because you're an AA flyer, you might want to consider flying to London on a cheap paid ticket to earn the Q-miles and then continuing on to somewhere else more expensive on the freebie.
That's what I did- JFK-LHR on one ticket, LHR-AMS on the UA award.