While you certainly do not want to get stressed nor feel rushed during your first time in LHR if you did do the booking with the 1 hour connection and missed it then BA will book you on the next flight (so long as you book all on the same booking). So there's no risk factor really (though your bags might not make it).

Also being on a WT+ booking, the domestic flight to EDI should book into J (if booked through BA.com - not sure about other sites), which basically means you will get to use the Galleries Club lounges at T5 - but to experience those you'll need to get the later flight as sammy mentioned.