Does Uk passport holder need a visa to travel around europe?

Turns out I don't 

Visas for short trips: you do not need one if you’re a tourist

If you’re a tourist, you do not need a visa for short trips to EU countries, Switzerland, Norway, Iceland or Liechtenstein. You can stay for up to 90 days in any 180-day period.

If you visit more than one of these countries within a 180-day period, check that you do not spend more than 90 days in total across all the countries you visit. That’s because most of these countries apply the 90-day limit as a group.

There are different rules for Bulgaria, Croatia, Cyprus and Romania. They each have their own separate 90-day limits. The time you spend in other countries does not affect how long you can spend in each of these countries without a visa.

https://www.gov.uk/visit-eu-switzerland-norway-iceland-liechtenstein#:~:text=If%20you're%20a%20tourist%2C%20you%20do%20not%20need%20a,in%20any%20180%2Dday%20period.