Have you tried/considered doing it online? It is a while since I did it, so, memory a little hazy, but, I seem to recall that all I had to do to open an "account" with HMRC was prove my identity, which was done via some form of Post Office link. Once that was done, I got a Government Gateway ID, and, a UTR (Unique Tax Reference).
As I say, it was a while ago, so, things may have changed.
I was, when I worked, a one man band, operating as a Limited Company (this is 15 years ago). HMRC were an absolute pain to deal with. They have actually improved, very slightly, IMHO, in recent years.
When Mrs
@BoldonLad retired HMRC made an incredible mess of her simple PAYE tax affairs, at one stage claiming she owed them several thousand pounds, and, sending her four (different) Notices of Coding, in one day. It took the help of our MP to get them off her back, it took two years, but, in the end it turned out, they owed her a four figure sum. That was 15 years ago.