This note appeared on the door of the café last weekend announcing that it was closing that “for a variety of reasons”. 
The City of London have apologised for any inconvenience. They are “seeking a short term solution” to so they can reopen the café as soon as possible. Their website will be updated with news of progress.
Meanwhile a tender process to find a permanent tenant for the café is about to start. If you want to express an interest in running the Queen’s Park Café, you can register on the City of London tender portal.
This Brent and Kilburn Times article gives some more background.