I arrived into BHX on SK2531 ex CPH on Sunday afternoon. I too saw the VC-10 (and yes, it was).
It was indeed parked on the western apron. My initial thought was it was probably in doing a trooping flight. It was an RAF example.
Boy oh boy, did it make some noise when it went out!!!
About 30 mins later, the TU-154 of Balkan Holidays came in too. Fantastic colour scheme.
Hope this helps.
EGBE