It sounds to me like a common issue I have had to deal with over many years working in the industry.
The problem was that whoever rebooked your GLA-LCY flight into LHR did not follow correct proceedure (ie re-protected you in the correct way), and becasue of this, the GDS only saw that there was no travel on the first leg - and so cancelled the remainder of the booking. By the way, I totally understand why airlines cancel itineraries that dont travel as booked - its to get around clever travel agents who work the fares system to their advantage - I remember years ago booking Concorde to MEX (with the NYC-MEX sector as "open") and halving the cost of the ticket, with no problem not travelling on the JFK-MEX sectors...
When I worked in an agency in an operational role, this sort of issue was generally rectified fairly quickly as the pax would call us, we would call our airline rep, and problem would be sorted (providing enough time given - ie pax checked in early).
Good luck - though I suspect that you wont need it - totally BA at fault.