Hi,
I too use the 'Midland' service between LHR and MME and often wondered about the ‘zig-zag’ route up and down the country. From LHR the route is generally as you state; Birmingham, Manchester, Sheffield/Leeds.
Just before Christmas last year I was on the morning flight up to Teesside (Fokker 100) when the crew made a fairly dramatic descent from the cruse altitude to about FL100 due to an air conditioning fault (it must have got to over 30 degrees C in the cabin). The descent was over East Midlands airport which I don’t normally notice – maybe the crew were considering a possible divert. Anyway, the reminder of the flight was one of the best I’ve had – superb ‘low level’ views over Nottingham, Sheffield, Leeds then over the moors and Middlesbrough/Stockton for a 23 landing.
The route is generally the same as you mentioned but I guess, like all flights, it’s subject to air traffic control’s demands so could route anywhere theoretically.
I too would like to know more!
QQ