A couple of things:

1. Hasn't BD stopped accepting connecting checked bags?
2. Wouldn't checked bags still have to clear customs at LHR before being transfered to a domestic UK flight?
3. I don't believe there is an onward baggage belt at T3, so if bags have to clear UK Customs at LHR, you'd have to take them over to T1 yourself.

Unless you're on a separate ticket, AC should be able to give you your connecting BD boarding pass in Canada. So, if one can get through this process in 15- to 20-minutes, a half hour in the Arrivals Lounge should permit you to then get over to T1, check your bags in at BD and clear security.

It's a tight connection though, unless taking place at a quiet time at LHR, of which there are few.

As suggested, you might just want to go right to T1 and us the BD lounge and its facilities.