I wish I lived close to LGW...or was going to be in that area at the time, but neither, I'm afraid. The trouble is, years ago, IRA bombings in London, they stopped even using lockers in train stations, and people are reluctant to hold things for other people (strangers to them)...I mean, even as part of a business. 10 years ago, maybe even longer, it would have been a no-brainer. I still see storage lockers all over the place; most just aren't used.
The only other thing (if you can't find any volunteers closer to LGW) is to mail the uneeded stuff back to yourselves, you know, like dirty laundry, and use the lightest bag you have, or just box it and fold up one bag to store inside the other. That way too, you would have space in the folded bag to get some loot to take back with you on the UK->US leg of your journey.
Well, as if you'd want to...I've never seen the dollar so weak!