Sometimes as a self employed person you are asked for a self employed registration number.
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
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