The idea was briefly assessed Peter, but IIRC the nature of the construction meant that a move was not possible.
A few years ago a similar proposal was considered (very briefly) for moving the tower at RAF Wigsley – similar structural issues and the fact that it had some sort of listing status, saw that option also kicked into the long grass.
As for a café, expect some fresh information about that project in the coming weeks – currently awaiting initial designs from the architects.