I cannot see how they will know how many days you are in the UK anyway unless you are connecting to/from international flights.
If you have booked with BA you automatically give your consent to releasing details of your flight to HMRC. Its been a booking condition for a number of years.
All passengers on IOM flights are photographed on entry to and exit from the UK. "Hidden" cameras are in operation. That's why until recently IOM passengers were bused to gate 100 in Manchester as it has the recording facilities and a convoluted walk-way to ensure everyones image is recorded.
I once asked at a BAA airport why the delay in boarding the IOM flight and was told that the only gate with the recording facility was in use for another flight, so we would have to wait until it was free.
If you go landside and use an ATM, pay for something with a card or use your phone, the revenue can prove you were in the UK from bank statements or telephone records.