Hello, if you haven't heard yet, banks are getting onto self employed people currently (there was a post about this on twitter). They are asking you to have business account, because we cannot use anymore personal accounts for any purposes.
I doubt it's anything to do with using a private account for business transactions. Two transfers into a private bank account would mean a massive leap to assume a private bank account is being used as a self-employed business account. By the way this wouldn't be illegal just a breach of the banks T&Cs which means the bank could close your account down but they would probably fall over themselves to set up a business account and rake in the fees.
If you take regular deposits it may be worth shopping around to find a bank offering an account with a 6 or 12 months fee free period and set this account up in a business name which you could give to clients. Ie. you would have a bank account in the name of Josephine Blogs Trading as Luscious Louise, you would then tell the client to transfer the money to the account details of Luscious Louise.
Your bank has probably restricted your account due to the "confirmation for payee" regime that banks have been pushed into putting into place during this year due to the amount of bank transfer fraud. See which explains about it all: https://www.theguardian.com/money/2018/oct/18/banks-to-check-account-names-to-beat-transfer
Only a suggestion that you might be just as well popping into your branch and speaking to an adviser and explaining the situation. They may close your personal account for breach of T&Cs or more likely set you up a business account but as there is no fraud involved they shouldn't be interested in holding onto your funds. If they do you could complain to the banking ombudsman but you would have to explain the true situation. Your bank may have to check with the payer that it's not a fraudulent transaction though.
The Money Laundering Regulations and the cost of fraud to the banks is onerous so they are just tightening up their anti-fraud procedures which any business would do to abide by the legislation and prevent the massive financial losses they were suffering.
Hope this helps a little.