After holding a UK Innovator Founder Visa (formerly Entrepreneur Visa), you may be eligible to apply for settlement (indefinite leave to remain) in the UK. Typically, you can apply for settlement after:

1. Spending 3 years continuously in the UK on an Innovator Visa.
2. Meeting the residency and other requirements, including not spending more than 180 days outside the UK in any 12-month period during the qualifying period.

Once granted settlement, you can eventually apply for British citizenship, provided you meet the eligibility criteria.