That's the motor racing clubhouse; I believe the one on the west side was also called the clubhouse (think I saw it in a plan published in 'Aeroplane Monthly years ago) for the flying club and it contains what looks like a control tower on top. I think Vickers built another tower on the east side also, the remnants are near the Concorde in the museum.
I did a school visit to Vickers (as it was then) back in about '66 and we were shown Barnes Wallis' office which he was still using (wasn't in when we visited though).