Your right to register as self employed while studying will depend on whether:
You have a citizenship from the UK or a state member of the European Economic Area (EEA)** or Switzerland then you can absolutely work for yourself, welcome onboard!
You are an International student in the UK on Tier 4 visa: unfortunately as per Immigration rules, you can’t work on a self-employed basis whilst studying. At this point so sorry to let you go.
**Inclusive of EU countries : Austria, Belgium, Bulgaria, Croatia, Republic of Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden
and also Iceland, Liechtenstein and Norway