Companies i know of that have hangers on the maintenance area are:
Northern Executive Aviation
Monarch
SR Technics
My Travel
apart from that its generally line maintenance carried out at manch either by in house maintenance teams or contracted out to companies such as storm.
I wouldnt concerntrate on just manchester Airport. You say you work for Airbus, Broughton or Filton site??? If your on the Broughton site try Raytheon down the far end of the field.
Also try other companies such as Eastern Airways in Humberside as they do all their own in house maintenance, Flybe down in Exeter, Storm aviation, you could maybe go contracting to gain experience