"She then makes a leap of logic – and faith in a civil service that earlier on she didn't even trust to set up a streamlined set of websites"
Having been dealing with the Government Gateway this morning, I also don't trust the civil service to set up a streamlined set of websites.
"Ah, the reason you cannot activate self-assessment with that User ID is because the Government Gateway single log in uses multiple log ins. I know that all services appear on the screen using both user IDs, which are both tied to the same Unique Taxpayer Reference, but you cannot use the one you use to do tax-free childcare to also do self-assessment. But don't worry, we will reset your password. Here are the first six characters of it displayed on a website, the other six are sent to you in an e-mail, you cannot change it, but don't write it down anywhere."