The Schengen area, covering most EU countries, will be introducing the Entry/Exit System although now delayed until 2025 and also the ETIAS travel authorisation later in 2025. These will affect all British nationals (other than double nationals and those with EU residency) to undergo additional formalities when entering the Schengen area.
The UK has announced that it will introduce an Electronic Travel Authorisation for EU citizens from 2nd April. See the article in The Independent of 11th September. This will be similar to the Schengen area's ETIAS and will cost £10. At the moment, the ETA only applies to certain Middle Eastern countries. The extension to most other countries, including the EU, has now been announced for April 2025.
The ETA can be applied for from 5th March 2025 and will be required for travel into the UK from 2nd Aoril 2025. An ETA will be required for all non-British or Irish passport holders including babies and children. An ETA is not required if the entry into a UK airport is for transit to another destination only AND the traveller remains "airside" (i.e. does not pass through passport control).
Although this will not affect British citizens resident in the EU if they travel into the UK on their British passport, it will affect those EU-resident Britons who are double nationals but currently only use their EU passport and British citizens who have spouses or children who do not have British nationality or a British passport.
However, if a British or Irish citizen does not have a British or Irish passport, they can apply for a certificate of entitlement to be added to the passport they do carry. This certificate costs £550 (price in January 2025) so it will almost certainly be cheaper to apply for a British or Irish passport instead. To find out more about application for a certificate of entitlement, visit the GOV.uk website https://www.gov.uk/right-of-abode/apply-for-a-certificate-of-entitlement.
To find out more about how the ETA application will apply, go to the GOV.UK website.