On 16 November 2016 the European Commission announced the establishment of a new European Travel Information and Authorization System (ETIAS) under which adults from outside the EU will be required to pay a 5-euro fee to apply online for prior authorization to enter the Schengen zone. Authorization would be good for 5 years.
Although EU members, the UK and Ireland have never been part of the Schengen zone.
The ETIAS system is expected to be in place by 2020, at which time (it appears) the UK will no longer be a member of the EU. So at least theoretically, British citizens wishing to enter the Schengen zone will be subject to the ETIAS application process and fees post-Brexit.
Because Ireland will remain a member of the EU, Irish citizens will be exempt from the ETIAS fees.