The National Archives at Kew holds a register to asylum patient files (MH 94) from 1846 to 1960. The register gives name and sex, name of the institution, and dates of admission, discharge or death.
Searching through MH94 allows you to find the date of admission of the patient to a particular asylum and the date they were discharged (possibly to another asylum).
Once you know the name of the asylum and date of admission you can find the patient in the admission register of the asylum concerned (which for a London one should be held at the London Metropolitan Archives if the records have survived) and from the admission register you get the patient admission number which allows you to access the patient's medical casebook.
Under the Freedom of Information Act you will be allowed to look at medical patient's case files under the 100 year year ruling, but if they are in a medical register with other patients and the casebook stretches into records towards the 1920s the LMA may reserve the right to do the search of the records themselves.
Without checking MH94 and without an exact date of admission you will need to check quite a few asylum admission registers at the LMA in the hope of spotting Ada, but I would start with Hanwell and Colney Hatch (renamed Friern).
The National Archives will also hold information on Alfred's service record in the Metropolitan police force.
The National Archives research guides are here.
http://www.nationalarchives.gov.uk/catalogue/researchguidesindex.aspLunatic Asylums, 18th-20th Centuries
Police, Metropolitan (London), Records of Service
Regards
Valda
