The short answer to this question is no. The slightly longer answer is that there are some very exceptional circumstances where it may be permitted but in most cases the answer will still be no.

The long answer on whether you can set up a business as a Skilled Worker

While here as a skilled worker you are subject to the following visa restrictions:

              “[…]      

(b) work is permitted only in the job the applicant is being sponsored for, subject to (c) to (e); and

(c) supplementary employment is permitted, providing the person continues to work in the job for which they are being sponsored […]; and

(d) voluntary work is permitted; and

(e) working out a contractual notice period is permitted, for a job the applicant was lawfully working in on the date of application; […]”

The relevant section to look at above when considering the legality of setting up your own business is (c). We then need to understand what is meant by the phrase “supplementary employment”.

Home Office guidance defines supplementary work as meeting all of the following requirements:

• “in either a job in Appendix Shortage Occupation List or a job in the same occupation code as the job for which the CoS was assigned
• no more than 20 hours a week
• outside the working hours covered by the CoS”

Credits: OTB Legal – Please view detailed answer on their website