I’m just trying to get my head around this too.

Isn’t the whole point of the set up at Heathrow that departures going out from A to B to C are sterile ie security screened whereas arrivals are not and never the two shall mix such that you wouldn’t be able to use the shuttle to go C to B to A departure gates - ie if going ‘back’ towards A it would drop you either at B gates arrivals / flight connections or A arrivals / flight connections. But at C you’d join the shuttle from the departures side (or landing pax could just get the lift up to departures and then miss security altogether, so it must be right you’d have to get on when others were getting off - ie join the transit from sterile departures side) and have to remain there when the doors close whilst they do the security sweep, so presumably the person doing the sweep would say you do realise you’re going to head to international arrivals / uk border?

Is it even procedurally correct that you ‘enter’ the UK when you have never left?!

I speculate but is it possible that if the OP had stayed at C gates BA would have ‘boarded’ at C61 using a bus (or the specific C bus gate) and dropped pax at jetty stairs for A17. I’m sure I’ve had something like this in Madrid before where the app said one gate, but screens where I was said something else and ‘boarding’ was onto a bus which took me and other (in this case connecting) pax in that satellite to plane.