I would be worried. If it was BA to BA, no problem. They have looked after me wonderfully well. However, you are talking about non-OW flight on a route that BA serves (and therefore you booked with BA's competition...) here. BA has no obligation to rebook you. Even more so if the delays/cancellations are outside BA's control. I strongly suspect you will be on your own if you misconnect.

With the issues at LHR such as fog, snow etc, I would not do this connection without a fantastic travel insurance that covers the situation in full.

In fact, for inter-alliance transfer on a separate ticket for personal travel, I have a policy of "no connection under 12 hours", so that the misconnect would be fairly unlikely.