mea culpa
Hi Camlobe, well done for being honest but don't beat yourself up about this too much.
A similar occurence happened to me as I flew back from Biggin Hill to Plymouth on Wednesday.
Biggin were using 03 and I turned left direct to OCK 1 mile after departure. I was at 2000ft and had the A/P engaged taking me to OCK direct. The air was pretty bumpy and the frequency was busy. Apparently I got close enough to the far Southeastern corner of Heathrow zone for Farnborough radar to ask me to turn South - I complied.
In busy airspace (the world and his wife were flying/gliding/helicoptering) it is easy to become preoccupied with looking outside for traffic avoidance.
We are all human and even the "perfect pilots" so intent on belittling those who fess up on the forum make mistakes from time to time.
You did the right thing talking to Heathrow and it sounds as though your apology was received graciously. Hopefully that will be the end of the matter for all concerned.
SB