The New British Civil War, also sometimes called the New English Civil War, has not broken out, as of June 2018, although some (such as Stefan Collignon) have claimed, or observed, is that Brexit has caused the semblance of a new civil war  and The Economist to suggest that Britain is suffering a very public nervous breakdown.  The present article is not about any fictional "hot" civil war--which is by its nature speculative and unknowable--but about the current discussion and speculation about such a conflict.
Why think a New Civil War might break out?
Discussion of a New British Civil War is, as of 2017, a staple of opinion pages and discussion groups with Michelle Clifford of Sky News warning of hysteria, mass riots and even civil war if the government ignores the will of the British people.  In a typical piece, Quora explains:
Unanimous consensus that although the UK is still deeply divided over Brexit, and the process of leaving the EU is a difficult one with a great deal of tension, some describe as a poisonous atmosphere while the situation is still not clear and several final outcomes are still possible.  It was noted that in Britain, the lack of easily available weaponry makes any kind of major violence unlikely, with only 559,302 firearms and 1,349,099 shotguns in Britain as of 31 March 2017. 
What might spark violence?
Conservative commentators such as Andrew Bolt have highlighted that the Islamist terrorist attacks, particularly the June 2017 London terror attacks may have indicated the start of a civil war and futher major incidents could provoke unrest.
Timeline of relevant events
- June 2016 United Kingdom European Union membership referendum
- June 2017 London terror attacks
- June 2018 Free Tommy protests
This list needs to be greatly expanded with events, e.g., Brexit protests, and notable instances of growing political intolerance (e.g., interruptions of speeches, increasing nastiness on social media, etc.).