You can do it at the LHR quite happily.

http://www.britishairways.com/travel/ba6.jsp/imminfo/public/en_gb has a list of what you'll need.

But in basic terms:
- Passport Information
- Your Address whilst in the USA (include a Zip code if possible)
- Country of residence

Keep this information as you'll need this pretty much every step of the way for your I-94(W), your blue customs form and at Immigration control (and if you're taking a cab to your your destination in ORD, to get the hotel/residence)