BA expressly will not check the bags across tickets (this does not interlining, because it is BA-BA). Thus, it is close to a certainty that OP will need to claim and check them at LHR.

Because of the no show risk on separate tickets, I would always allow at least triple the MCT. This accounts for all but very serious delays. The idea of trekking around London for the day is a good one, but you do have to consider whether the two children will be in any shape to do so if they have had a very short night of it on the hop from AUS to LHR.