Going to Paris on British Airways which stops in London

"Brexit" has not even begun to be negotiated yet, and even if it had, it has nothing to do with the matter. If are changing within the same terminal, you don't really enter the UK and you get your passport check and stamp entering the Schengen Treaty Zone in Paris. The UK is not and never has been a Schengen Treaty member, so there has always been passport control between the UK and France. After "Brexit" nothing will change.

Now if you had to change terminals, you'd enter the UK and get a passport check to enter, then another one to leave.

Just wanted to mention we flew from Canada to Amsterdam this year and connected thru LHR. We had to change terminals, but because we had carry on luggage only, we followed the signs for secure connections and didn't have to go thru a passport check - had we checked our bags and had to pick them up, we would have had to go thru the passport line. (Thanks Frank II for giving me all the info on that).

Of course, upon making the secure change to the other terminal (we had to wait at some doors that were locked until the terminal transfer bus came along) we of course had to go thru security again. But it took just under an hour to deplane, use the bathroom, find the transfer bus, get to the next term, get thru security and then we had 3 hours to kill until our next flight.

Just a quick add - we didn't have connecting flights - they were two separate airlines/booked separately. Not sure if you have a connecting flight and if your luggage is checked thru that you can skip the passport line...

Yes, you go through passport control in Paris, which is where you enter the Schengen Area.
In London Heathrow you transit "airside" and do not legally enter the UK, no passports (but ID checks). Unless this is two separate tickets, in which case you have to enter the UK and check in again for the second flight.

For the record - we flew on two separate tickets (Air Canada and Brit Air) but did NOT have to go thru passport control at LHR - because we didn't have to retrieve bags. We also checked in at home before leaving and had the boarding passes printed.