<font face="Verdana, Arial, Helvetica, sans-serif" size="2">Originally posted by pinniped:
(Granted, I've never tried to check a bag all the way through from MCI-LHR when doing this. Maybe that would be problematic...or maybe it wouldn't.)</font>
It would work as long as the two airlines have an interline agreement, just show the agent both tickets and explain what you're doing, and your bag will be checked all the way through. I've done this twice, and other people do it all the time (many threads on FT mention this).
You still may be left unprotected if you miss your other flight, especially if different airlines are involved, but that's a different issue.