There is no longer an official HM Revenue & Customs (HMRC) ‘arrival form’ for you to complete when you arrive in the UK.
However, if you want to work in the UK, whether as an employee or self-employed, then you will normally require a National Insurance number.
If you are employed, you may also need to complete a starter checklist for payroll purposes.
If you are self-employed and earning above the trading allowance, you will generally need to register for self assessment and Class 2 National Insurance contributions.
You might also need to register for self assessment for other reasons, depending on your circ*mstances.
See Also
What is a BR Tax Code?