Hi
Looking at the newspapers, there is a John Clay, consulting enginer, who was charged with forgery in 1869
Bradford Observer, 18 June 1869
SERIOUS CHARGE AGAINST A CONSULTING ENGINEER.Yesterday, at the Hull Borough Police Court, before the stipendiary magistrate, a young man, of gentlemanly appearance, named John Clay, was charged with uttering a forged bill of exchange for £70 10s. The prisoner, who is consulting engineer in a large engineering establishment in Hull...
The case ended up at the York Assizes, where he was found gulity and sentenced to five years penal servitute.
Age was 36, which is in the right ballpark.
So there seem to be quite a few records for this chap in the criminal databases online, but I don't have access to them at the moment.
However, it seems he was sent to Broadmoor?

Though he may not still be there in the 1871 census?
Entries in ancestry's England, Criminal Lunatic Asylum Registers, 1820-1876
Name John Clay
Conviction Age 36
Birth Date abt 1833
Charge Forgery
Sentence 5
Conviction Date 29 Jul 1869
Conviction Place York
Something to investigate perhaps.