I don't think there has been anything similiar to the Nuffield analysis quoted here specific to mental health beds but its definitely an area that needs greater investigation.
There was some analysis last year about the decrease in mental health beds more generally across the system (Guardian coverage here) and current occupancy levels remain above the recommended level (Royal College of Psychiatrists analysis here) but suspect that picture is more complicated regionally, you would imagine some areas are under much more strain than others. Also today's new National Audit Office report looking more broadly at mental health performance highlights bed occupancy issues.