Shell, according to
www.sortcodes.co.uk the sort code is registered to HMRC, so it is real.
Suff, I think it is a lucky dip on their part.
Millions of letters are sent out by HMRC and as you will know it is easy to scan one to something like pdf and then change it to suit one's needs. This is what I believe they have done. I am sure they do not know my full NI number, that is why it is just showing the first and last letter with the rest being asterisks. Those can be based on my DoB and location when it was first issued all those years ago. Names and addresses are easy to get from many different sources.
I made a PPI claim through an agent about seven or eight years ago, as did many others, which was long before data protection was as strong as it now is. I suspect that a lot of our details are now in the wild and this is where these new scammers are getting information from. Many of the agents who were set up to handled PPI claims no longer exist as their job was done, however, they might not have been diligent in destroying or securing their old records.