A. All self-employed people in the UK are required to be registered for Self-Assessment and then you are issued with a UTR or Unique Taxpayer Reference number. This number is usually presented as a pair of 5 digits. eg 12345 54321
If you have been asked as a self employed person for a self employed registration number. Give them your 10 digit reference number from HMRC.
Strictly there is no such number of this name but for professional UK tax purposes the number that you need to give them is your 10 digit UTR or Unique Taxpayer Reference number or self employed tax reference number. This number is usually presented as a pair of 5 digits. eg 12345 54321 You can normally find this on any recent letter / statement / reminder from HMRC.
Some employees outside the scope of UK self-assessment have not yet been issued with this 10 digit UTR and so rely on their NINO or National Insurance Number and / or your employer PAYE tax reference number that usually starts with a 3 digit code to identify a UK tax office. eg 123/J321Z