You lose nothing by asking (and I would ask), but the rules are there. If you don't have a H, M, B or Y fare then you are not entitled to this. This doesn't mean you won't get it, just don't expect it, especially ex-LHR.

There is a reason for these rules - *A are out to reward people spending serious amounts of money with them. I don't think it's reasonable to expect an upgrade when you have a cheap web fare booked in T class or something similar.