I am looking at airline reservations from JFK to Edinburgh for July 2019. How long does it take to clear Immigration or Customs at Heathrow? Then how long to get to a connecting flight to Edinburgh? I am looking at using British Airways as that seemed easier than flying through EU countries and having to go through Customs/Immigration twice. This travel time will only be about 3+ months after Brexit begins to takes effect. Thanks for your help!
If you are looking at a BA connection within Terminal 5 it is relatively straightforward; a bit more involved if arriving in at T3 as you will need to take a bus airside between the terminals. Immigration is separate for connections from people finishing at Heathrow, although security is merged in with passengers starting from there. Minimum connection time is 60 mins for T5-T5 although having it a bit longer will make it less hectic. Checked bags (if any) will on a single ticket not need to be collected until arrival at EDI.
If you go through a non-UK airport (for example Amsterdam Schiphol), then you do not go through immigration there, you stay "airside" and go through UK immigration when you land in the UK.
This is the current and future situation, because the UK is not and never has been in the Schengen Area.
Why not fly AA on a direct JFK-EDI flight?
It is very straightforward in terminal 5. You follow the “flight connections signs”. There will be a location where it splits into two lines. You will go to the UK domestic connections line. You go through passport control, have a biometric reading done in conjunction with your boarding pass for the next flight, go through security, and are in the terminal ready to get your next flight. 30 minutes to an hour has been my experience.