The law is a little vague. It says that someone convicted of money laundering may be disqualified for acting as a company director (ish). I assume that would be part of sentencing, or it may be a decision made by Companies House (or whoever vets that). Certainly ex-prisoners can start business in general.

A bigger issue may be things that require credit checks, like business loans, bank accounts, insurance, etc.

Some good advice here: https://unlock.org.uk/advice/things-think-becoming-self-empl...