To the OP, there are a variety of reasons why your seat may have changed (or have been changed).
But since it was not a single "shift", but you were moved on both legs, the most likely explanation is that the reservations system cancelled your seats and auto-stuck you in some random seat.
A. Random Seat Shifts
This can happen for a variety of reason, such as (1) a ticket number being put into the (unticketed) reservation, (2) the ticket being reissued, (3) any kind of flight time/number change, which require the reservations agent to "ok" the change. Any of the above may lead to you being booted of your seat and given a random one again.
B. Deliberate but Anonymous Seat Shifts
Another reason is someone changing the seat (maliciously, or for fun, or a BA insider doing it to put someone else in your seat). But to do this with no trace, would require them doing it in in MMB (so having your PNR and surname - very easily accessible), which should result in your receiving an email confirming changes to your booking. Always look out for these, if you haven't made any changes yourself.
C. Official Seat Shifts
Finally, you could have indeed been moved by BA seating to accommodate a Prem or VIP.
With the right status and a big enough issue (not just I was moved from 1A to 1K, but a party of 4 perhaps being scattered around the cabin), you will be able to get someone to investigate the booking, the date the changes were made, by whom, what triggered the move, who is now in your original seats, so at least you know whether it was a RSS, a DASS or a OSS, and you may be put back in your original seat.
I suspect you will not get this kind of help and you will be told it was an "equipment change".