If the flights are on time you will be fine.
Since you are traveling Club Europe out of LHR
you can use the priority line for passport check and security (it should be the farthest to the right), though, as it was mentioned, it could be a bit busy at times.
After you clear security you could even have enough time to stop by one of the BA
lounges (as you come out of security turn left and there should be one really close there just in front of you... I think this should be the North lounge). I do not think I ever had to walk/travel more than 15 minutes to get to my gate from the BA
(North) lounge, even if I had to go to another concourse.