I see the gym has now closed and planning notices say that they want to demolish the building.

Any thoughts on this?

I wonder if this will affect Rubadubs next door?

I believe this application is from last year (DC/11/77463)
This application has now been withdrawn by the applicant, following objections from neighbours and the Forest Hill Society (see here)

There was a previous application (DC/08/68497) that was granted, so work could begin on residential units on the first floor and a new second floor.