If you open the link,https://www.wirral.gov.uk/my-services/le...s/cammell-laird
On the right hand side, Downloads, Attachments, List of Cammel Laird
ships, the list of ships your dad may have worked on will be amongst them. To give you a time scale, Windsor Castle, Lairds number, 1287, that would be around 1959, Hms Birmingham, 1973 ish.
If he started serving his apprenticeship in 1961 at 16 years old, the chances are he wouldn't have been on a ship until he was 18. Its also possible he spent his time in the yard in the assembly bays and never actually worked on the slipways where the ships were constructed. Even so he still would have been involved in building a ship.
If he's anything like me he won't remember half the ships he's worked on, or want to.