It's true that you can't get AA credit for BA trans-Atlantic flights. The reasons have been discussed at length in other threads.

However, you can get credit even if you forget to give your number before the flight. Go to aa.com, log in to AAdvantage (you'll need a PIN to do this), go to View My Miles, and click on Request Credit at the bottom of the page. You'll get a form to fill in for AA flights and instructions for handling other missing credits (partner airlines, hotels, etc.). You can also do it by mail or fax without a PIN. The folks who get the forms do their job well.

Other airlines have slightly different procedures but they all have one. Some even allow retroactive credit for flights within a reasonable period (90 days is typical) before you enrolled in their program.

Also, all is not lost with your recent trip if you changed in London. If so, you DO get full credit (base miles even count toward AA elite status) for the European flight. It's only the trans-Atlantic flight that doesn't count.