Tl;dr: The quotes are a mixture of provocation, sloppy word choice and metaphorical use. A true civil war is prima facie inconceivable in the UK. Missing root causes and missing recruiting potential make it impossible.
A note about forecasts. It is no accident that this is the term used for weather; there are strong similarities. We know that "prediction is very difficult, especially about the future"; while our factual knowledge as well as our theories are surely deficient, I suppose that the sheer complexity of the (political, sociological, technological, ...) system whose development is to be predicted severely limits the scope of any prediction in principle. Complex systems are often non-linear, or chaotic; small, early deviations quickly escalate and lead to completely false results for later points in time. E.g., a few thousand more votes in one state or another during a presidential election lead to an unexpected feminist anti-harrassment movement. Historical development has, underlying tendendencies notwithstanding, a strong chaotic element. Any attempt to attach a specific fraction of a percent likelihood to certain events is a fundamental conceptual error.1
The Term "Civil War"
Before we actually discuss possible causes for a civil war and investigate whether some of them are present in today's UK, let's first define what a civil war is (emphasis by me):
A civil war [...] is a
war between organized groups within the same state or country. The aim
of one side may be to take control of the country or a region, to
achieve independence for a region or to change government policies.
[...]
A civil war is a high-intensity conflict, often involving regular
armed forces, that is sustained, organized and large-scale. Civil wars
may result in large numbers of casualties and the consumption of
significant resources.
To put this definition in perspective: According to Wikipedia, the Troubles in Northern Ireland are 'sometimes described as a "guerrilla war" or a "low-level war"', but do not appear to qualify as a civil war, probably because the high intensity was missing. After all, life mostly continued normally for large parts of the population. Contrast this with the situation in countries with present or past full-fledged civil wars, like South Sudan or Sierra Leone, which both have millions of displaced people and suffer from famines, disease outbreaks and other humanitarian emergencies.
For your question it is particularly important to distinguish the concept of civil war from other types of unrest like riots, terrorism, rebellions, coups etc. These lack organisation, scale, and/or are not sustained or intense enough to qualify as civil war.
With this picture in mind it appears that the talk of civil war in the journalistic texts you quote is a mixture of
- provocation, especially when activists are quoted;
- sensationalism, paired with sloppy journalistic craftsmanship — they didn't even read the Wikipedia article!;
- metaphorical speech ("there is a civil war in the Labour Party").
Even before we explore causes of civil wars, a situation comparable to places with actual civil wars appears exceedingly unlikely for the UK.
Causes of Civil Wars
Common sense already dictates that a grave dissatisfaction is the root cause for any rebellion, let alone a civil war. The Wikipedia article lists a plethora of possible sources for dissatisfaction, material (hunger, poverty) and immaterial ones (religious and ethnic conflicts, dysfunctional administrations, bad governance).
Interestingly a third factor appears to play a large role: Civil wars are more likely when it is easy to recruit "foot soldiers". Contributing factors are poverty, a large, [young], badly educated population, and trivialities like rough terrain [probably resulting in weak governmental control].
It is obvious that very few if any of these causes apply to the UK, now and in the foreseeable future.
Yes, there are grievances and a sense of a lacking ability to participate politically; these are why we are having this discussion. But first of all the grievances are minor and, considering that the UK has free and secret elections, not comparable to the ones fueling civil wars in other parts of the world.
Secondly, all other causes are missing. While poverty is relative, the UK is one of the richest nations in the world. Even though large-scale changes in the political landscape happen fast compared to the second half of the 20th century — washing up inapt or dubious political personnel and generally contributing to a sense of insecurity —, the political institutions as such seem stable enough; administration and law enforcement are certainly working well. Education levels are high. The population is aging and shrinking. There is no way to recruit a rebellious army (of young men!) for any sustained amount of time.
While there is potential for religious tensions between Christians and Muslims, general consensus seems to be that a civilized way of living together is the British way to solve them. The terrain is not overly rough, with the exception of parts of Scotland (which indeed did have a civil war in he 17th century!).
As mentioned in the beginning, a civil war situation in the UK is already prima facie hard to imagine; after examining potential causes for civil war it is as good as impossible.
Rebellion, yes. Burning cars, terrorist attacks, riots: yes. But civil war: No.
1 It is already impossible (and, consequently, all attempts to do so have wrong results) to make an accurate prediction of the likelihood of a catastrophic failure
for a single nuclear power plant. One such event in Fukushima significantly changed the course of Germany's energy policy. This is
although all technical facts about the power plant are knwon and documented in great detail, and the theories of the nuclear and non-nuclear processes governing its behavior are complete and correct. (Contrast this with sociological processes.) Part of the equation surely are the human operators. The behavior of this comparatively well-understood, well-documented artifact plus human operators is already too complex to accurately predict under all circumstances.