Sole traders are not legally required to take out any kind of business insurance unless:
They employ people, in which case Employer’s Liability insurance is compulsory.
Professional Indemnity insurance is a legal requirement of their particular profession. This is relevant to accountants, financial advisors and other professionals who are members of certain trade associations.
The business uses motor vehicles, in which case Third Party Motor insurance is required as minimum cover.
Even if you do not fall into the above categories, you may still wish to protect yourself from potential liability claims from third parties. Take a look at this guide from the Association of British Insurers for more information.