I think any flight between UK to USA will be very strict with what you carry.
I was only allowed to board the plane from UK with only a hand carry baggage which is my labtop the size restriction that you have mentioned, but after boarding the plane, i saw many other passengers with a hand carry baggage much bigger than what they have stated that is allowed.

But those passengers are heading towards Sydney so maybe the ground crews had closed one eye.
When i came back from Sin to UK, i was allowed a hand carry bag plus my labtop which means i had boarded the plane with 2 baggages.
I am not sure about yours so maybe you can call the airline and check with them.
We even need to remove our shoes and place it on the X-Ray scan.
www.baa.com
Best Wishes