For SSimon2007,
Definitely check all the requirements in Apple's Support article:
Universal Control: Use a single keyboard and mouse between Mac and iPad
... keeping in mind that there's essentially no flexibility in those requirements. Especially having to be logged in with the same Apple iCloud ID on both systems (not a "Managed ID"). And that Handoff is explicitly enabled on both the Mac and iPad.
Be sure to check all three of the Universal Control checkboxes on the Mac, including "Automatically reconnect .."
If you still have a problem after that, your problem sounds like a problem I had with Universal Control that went away after I made sure that (in Preferences -> Security & Privacy -> Firewall -> Firewall Options on my Mac) wasn't Blocking incoming connections from both:
rapportd
Universal Control.app