I was originally on 254 but got to T3 early and asked if I could be put on 256. CSO made a phone call and said no problem. Got my BP issued and went to queue up for security control which took 45 minutes.
Onboard the plane I had a whole row of seats to myself. I have not had such an empty cabin on the LHR route for a long long time!

F was half full. J was completely full. Y was half full and almost everyone had empty seats beside them. I would say that J is very often full due to the huge amount of business travellers so the J cabin is likely to fill up regardless of the amount of seats.
The loading very much depends on the month and day of the week. In your case,
kaka, when (and on what day of the week) are your parents planning on travelling? :-: