The Small Ships Register is Part 3 of the UK Ship Register. GOV.UK says it's for pleasure boats under 24 m owned by people living in the UK at least 185 days a year, costs £35 for 5 years, and proves the boat's nationality when sailing outside UK waters. Businesses can't use it, and it doesn't record ownership or mortgages.
What a surveyor checks
The SSR number on the certificate and its expiry, and that the boat carries the number. Because the SSR isn't a title register, a buyer relies on the bills of sale: PBO quotes a broker who looks for at least five years of clear title. See Part 1 registration for the title register.
In the report
"Registration: Small Ships Register, certificate seen and in date. The SSR doesn't record ownership; title to be established from the bills of sale."