All 4 terminals at LHR are "international" -- yes, every single terminal there has international flights. You can choose to enter the UK, clearing immigration and customs, or stay airside in transit, using the FCC (Flight Connections Centre). Either way you are subject to the same security check at LHR (and the same rules, e.g. limit on carryon size and contents, for example no foreign duty free liquids are allowed in carryon, they must be in checked baggage). If you have contraband, you are given the choice to have it confiscated or abandon the bag or go landside and check it; the FCC has a huge pile of trash filled with some amazing things that people have abandoned (rather than miss their connecting flight). Staying airside in transit is sometimes better/faster than going landside, sometimes it is slower/worse (presuming you don't have any visa issues with the UK and aren't on a wanted list). This month LHR has been a nightmare with huge lines and lots of problems (beyond the fog). It is not fun anymore. I'm afraid you will come to regret your long routings, which are very tiring (I've done them, and they are tiring even in F, never mind J) and this trip will seem more like an ordeal than a special treat. Good luck and do lots more research to mitigate the problems and make it work better.

ps. I've taken YYZ-LHR a dozen times (mostly in F, sometimes in J as BA uses 3-class planes for part of the year), and it is a terrible flight (compared to ORD-LHR for example). Too short to get any sleep, and they serve breakfast 2 hours before landing in J -- absurd. So even if you aren't eating (and you shouldn't be, there is lots of better breakfast in the LHR lounges) you are woken up by all the clatter. Plus the YYZ lounge is very shabby, and the food is dismal (used to be very good until 2 years ago, then the lounge manager and chef changed, and it is consistently poor now). YYZ-LHR seems to be the worst of the BA routes to Canada at the moment (YUL and YVR are much better, and the similar DTW-LHR and ORD-LHR are also better -- strange that YYZ is so bad, but I'm sure there is a reason).