I'm interested in the impact of utilitarianism upon English psychiatric care by way of the philosophy's influence on social reformers. More tenuously, I want to know whether and in what ways utilitarianism shaped theoretical writings on the nosology/aetiology of madness within the second half of the 18th century and the first half of the 19th amongst physicians.
I've done research in this field, and believe the simple answer is that utilitarian social policy in eC19 moved in the opposite direction from developments in clinical psychology at the same time.
For example, the utilitarian creation of the New Poor Law in 1834 made workhouses more austere, with reduced diets and families separated by sex, not to mention adding the useless labor of the treadmill and similar innovations.
At the same time, clinical mental medicine was moving toward more compassionate care of the insane, with asylums modeled on domestic life and an elimination of physical restraints. In Britain, this began in 1796 with the introduction of moral therapy in the York Retreat founded by the Quaker William Tuke. In 1839, non-restraint moved into the first large county asylum under the directorship of John Conolly, at the Middlesex County Lunatic Asylum at Hanwell.
On developments in medical care of the insane during this period, see the following for a good starting point:
Andrew Scull, Charlotte MacKenzie, and Nicholas Hervey, Masters of Bedlam. The Transformation of the Mad-Doctoring Trade, Princeton University Press, 1996.