Unlike Part I registration, I don't think the Small Ships Register have a public search facility. But to find out for sure, contact them in Cardiff on 029 207 68206. As you doubtless know, SSR doesn't prove ownership.
I found them very helpful when I bought my current boat. They were able to advise all previous owners but this assumes that all kept up registration and notified the administrators.
Thanks chaps. It's not for me. A friend phoned from Bembridge as his boat had been hit and the chap sailed away. someone got the name and the ssr number. I phoned Cardiff and they will supply the info on receipt of a letter and a £5 cheque. Just hope the info is up to date.