as others have noted, AA is pretty good about award availability. i've never had a problem, even before i was elite.

...but you are asking for four seats during peak season, so book without delay!

just out of (a little more than) curiosity, what is your departure city or gateway? the reason i ask is that for some people using miles for coach travel to london - especially during peak season - does not always represent the best value.

if you live in the midwest, pacific northwest or the west coast, it may be a good deal. if you're coming from the east coast, you're usually better off buying a ticket (earning miles on that flight, as well) and using your accrued miles for a higher value option like travel to hawaii or for several domestic tickets.

of course, if the miles must be used or no other trips are planned, then by all means use them to get the tickets to london.