From https://www.gov.uk/guidance/immigration-rules/appendix-student
ST 26.5. A Student is not allowed to do any of the following:
(a) be self-employed or engage in business activity unless ST 26.8 applies;
ST 26.8. A Student may be self-employed, if:
(a) they have applied for permission on the Start-up route; and
(b) that application is supported by an endorsement from a Start-up route endorsing body which is a higher education provider with a track record of compliance; and
(c) the application was made when the applicant had permission as a Student; and
(d) a decision has not been made on the application, or where the application has been refused, any Administrative Review against a refusal has not been finally determined.