I can't speak to how things were in 2023 but today you do not need to visit Estonia.
Registering a company in the U.K. is very easy but the tax treatment is less favourable compared to Estonia. The U.K. leaving the European Union is also disadvantageous (although the full consequence of that is yet to be seen). All company filings in the U.K. are public, much more information about your company is public compared to Estonia.