Yes, there is a separate BF checking line at CLE which operates for the CLE-LGW flight every evening. (I'll check out how well it works tomorrow night and let you know!).

Regarding the luggage issue - I had a similar problem a while ago trying to fly to Buenos Aires via Sao Paulo - switching to TAM from CO in GRU. They would not check my luggage all the way through from CLE - but very luckily, the BF Concierge at GRU was very helpful and found my luggage for me, re-routed it to EZE manually, and it arrived with me on the TAM flight.

I'm afraid the outsourcing of ticketing agents really is not helping the process...