Cityguy1 please consider the following possibilities:
1) you check your bags (and yourself incidentally) in for LHR-DOH in the morning. Because you did not check-in for the MAD-LHR leg the airline could cancel that flight.
2) You leave your bags in left luggage in LHR and fly LHR-MAD. You check-in at MAD for MAD-LHR-DOH with no checked luggage. At LHR due to security reasons you are not allowed to check further bags in.

Please remember the security mantra 'Passengers and luggage fly together'.

I am not saying that these things will happen just the the ambiguity of the rules appear to allow those interpretations.