If you're on one ticket (which is suspect is the case), then the easiest way to make sure you can pick up your bags is an airport change. Fortunately in London that's pretty easy with LHR and LGW. I do this sometimes with Tokyo as well using NRT and HND to force a short check. Overnight generally works too, but I have had the machine spit out through checked tags (think it was under 12 hours in all cases) and had to get the agent to manually change it stating that I needed the checked bags during the overnight. (Note it wasn't always on a throw away ticket I've had this happen but seems to be the norm if there isn't an airport change and it's 12 hours or less)

Now having said all that, if all else fails, they are not supposed to allow your bags to stay on the plane if you don't board the flight. If you have a sufficient layover then you could easily walk up to the baggage counter on arrival at LHR, tell them you feel sick (think sinus congestion so you can't equalize your ears, not necessarily anything that's going to get you sent to the health officer) and won't be making your connecting flight today and they could get your bags, though it may take a while.