If Peter wasn't listed as being adopted, then his name did not change. It therefore follows that approx. 20 years later or so that he probably married.

There are a few marriage entries for Peter Lee in Sheffield.

1. Peter Lee married Jenet Lee December 1987 Sheffield Vol 3 Page 999.

2. Peter Lee married Caroline Doyle Apr. 1988 Sheffield Vol 2 Page 1302

3. Peter Lee married Jannette M. Biddulph Jul-Aug-Sep 1982 Sheffield Vol 3 Page 1560.

Don't know if any of these are the Peter Lee you are looking for, but perhaps a place to start. Ordering copies of the marriage certificates might give you additional names to follow up.

Are you near Sheffield? They have family history services available see:
https://www.sheffield.gov.uk/libraries/archives-and-local-st...