The main database:
UK Lunacy Patients Admission Registers 1846-1912
Also:
England and Wales Criminal Lunacy Warrant and Entry Books 1882-1898
England Criminal Lunatic Asylum Registers 1820-1843
(this one is a very small database.)
Looking at the main database, ancestry's index includes a data item called "Institution Place" which seems to be a county name that they have deduced from the name of the asylum. This county name can be completely wrong, so I would recommend ignoring it!
For instance, I found my relative Wm Bowskill listed at Fisherton, which it shows as "Institution Place - Ayrshire, Scotland" but it should surely be Fisherton House Asylum, Salisbury, Wiltshire, which accepted criminal lunatics before Broadmoor, according to Wiltshire Council's website. Very interesting for me as I have long been wondering where my relative was before he was placed at Broadmoor.
(Speaking of Broadmoor, ancestry have relocated it to "Pembrokeshire, Wales"!!!)