BA Franchise carrier - Sunair from Denmark operate a number of inter European routes not touching the UK on BA flight numbers
bmiRegional - Operate various services across the EU from places such as Munich
Eastern operate within France and charters.
Easyjet (UK) extensive route structure
Thomas Cook and Thomson both operate their UK fleets in other domains including long haul however both are actually German owned businesses.
Now here is one you might be surprised by - Air Berlin are registered in the UK !
IAG group utilise their brands according to domain.
Other odd ball BA has a French subsidiary Openskys operating between Paris and New York
Flybe operate franchise services for SAS, had a Scandinavian business and will operate from Germany
Numerous UK cargo and package aircraft fly all over the place every night
Yep Brexit could have an effect if we can't retain the Eu open sky treaty condition.
Easyjet would almost certainly relocate .