The worry is not only cross-breeding but what diseases and parasites they may be carrying.
Is anything being done to combat this problem and would a .243 calibre rifle be suitable to control them if they appear?
WILD BOAR SHOOTING
AIt looks like the spread of wild boar to most parts of the country is inexorable, with the problems you mention as well as crop damage and encounters with the public and their dogs.
There has been reluctance from Government to shoulder responsibility and management decisions have been left to individual landowners and occupiers, though advice is offered.
Feral Wild Boar: An Action Plan can be found on the Natural England website.
There is also a Wild Boar Best Practice Guide at www.wild-boar.org.uk
Basically, though, it has been left to communities to sort out their own troubles.
Boar are powerful and notable for a disregard for fences.
A full-strength electric fence does have a deterrent effect, but will probably fail if an in-season sow is on the other side.
Your .243 rifle is not heavy enough for purpose.
Boar have heavy bones and a wounded beast can be very dangerous.
The .308 or its equivalent is needed with bullets designed to penetrate.
When applying to the police for a new rifle on your firearms certificate, mention that it is for boar as well as other quarry.