Hi Richard
It might be worth looking for Patrick as well as Peter as these were often used interchangeably in Scotland. This family, in the 1841, caught my eye:
Main Street, Gorbals, Glasgow, Lanarkshire
Harkins
Roseann, 35, Cotton HLW, b. Ireland
John, 20, Cotton dyer
Patrick, 18, Cotton dyer
Roseann, 15
Mary, 10
All but Roseann, snr, b. Lanarkshire
There isn't an exact match for him on the 1851 so he might be yours.
Gadget