All of AI's facilities at LHR were sold to BA during the Rajan Jetley era for a pittance (can we say Carl Icahn?). This included everything from the sizeable AI cargo warehouse down to office space at LHR. Jetley then proceeded to lease the same stuff back from BA.
During this time, AI also signed a ground-handling agreement with BA whereby all AI ground services would be handled by BA. However, when BA terminated its ground handling operation at Terminal 3, AI rehired the same staff that it had laid off and bought back the space from BA at market value (approximately 4 times the price they sold it for). AI now handles all of its own ground services at LHR with the exception of emergency maintenance (BA) and luggage handling (EI).
The slots issue is one that screams HYPOCRITE about BA/BAA. I will drag up the details and post them here. As for maintenance, BA has done a fairly decent job helping out when needed, unlike UA who essentially reneged on their contract for maintenance at ORD.
"The A340-300 may boast a long range, but the A340 is underpowered" -- Robert Milton, CEO - Air Canada