I find LHR pretty fast, 20-25 mins from wheels down to standing outside with luggage. At least at T3. That said I have a UK passport but you likely won't be clearing immigration there.

That said, no guarantee you arrive in time as stated. It's one PNR so as you said just look up some alt. options to feed agents in case you misconnect. I know you said only one other route works but consider if that flight is full ..