History tells us that a relatively small minority of zealots can indeed sieze power but I think the number in this case is much too small even before you take into account that the examples you cite are not equivalent. But here's my bigger issue...
Let's hypothetically say the entire Muslim population of the UK wants to undermine our values. This is obviously not the case but let's just imagine it. That would be about 6% of the population. Now compare that to the number of people who currently when asked, say they would be happy with an authoritarian leader who could bypass parliament and the rule of law to 'get things done'. Depending on the survey and questions asked, that percentage is between 15 and 20%. In other words 3 times the total of the entire Muslim population of the UK.
We are a liberal democracy, we started moving towards this in the 1200s and achieved it in 1928. In our schools we explicitly teach British Values and there are 5 things that we define as fundamental to Britishness.
1. Democracy
2. The Rule of Law
3. Individual Liberty
4. Mutual Respect
5. Tolerance of different faiths and beliefs
This is literally what we teach our children Britishness means, what we mean when we talk about our 'way of life'.
Yet the data suggests that currently 15-20% of our population reject or do not value the first two of those fundamental aspects of our way of life and would be comfortable with an authoritarian strong man taking control instead. The proportion of the Muslim population who'd be up for creating a theocracy is tiny but this group of people are not. So I don't give a toss about the odd Islamist head banger because they're not a credible threat to our way of life, whereas this group of people possibly are. They are a minority but a big enough one to potentially cause significant damage and take over in the way you describe. So I want to understand them more. Who are they, why do they feel like this, how far would they be prepared to go to undermine our way of life, who do they gravitate towards politically? How cohesive is this group of people? How well organised/funded? To your point, do some of these people already have access to the levers of power in this country?
This should be our national conversation, we're beginning to see what happens in the US when you elect and tolerate someone who's not interested in democracy or the rule of law. Yet we have maybe up to a fifth of our population who seem ok with the idea. Imo that's what we should be talking about.
I am not suggesting for a moment we are in imminent danger of a muslim theocracy, as you say the numbers are of course too small. The point I was making and I think you accept is that a small highly motivated minority can take control of a passive majority and exercise power. Therefore there is no comfort in the numbers that suggest only a minority of UK muslims prefer Sharia law. We saw at the last election in that the muslim vote was being re-organised along more sectarian lines , this will be an opportunity for militant Islam and they will have scant respect for the British liberal values you mention. This will pose a threat to our way of life in regard to tolerance, free speech etc.
As to your second point, I do wonder sometimes if our version of democracy will survive but usually convince myself it will. I am not surprised therefore that some may not reach the same conclusion.
Democracy surely has to be seen to work , the will of the majority should prevail and be seen to prevail. Unfortunately in recent times we have seen the opposite. Whatever your opinion of Brexit, the country voted to leave the EU, yet this democratic vote was undermined at every turn in our own Parliament with the complicity of the Speaker of the House. The establishment conspired to thwart the democratic will of the people.
The majority of the electorate want to see considerably lower immigration, both major political parties know this, they both promise to deliver this yet in government they do the opposite.
At the last election, the Labour Party won 63% of the seats in Parliament with barely 33% of the vote, is their agenda the will of the people? The system does not work.
That said I would suggest that the biggest driver of the anti - democracy sentiment you mention is that the problems of the Country seem intractable. None of the major parties or politicians inspire confidence or have any sense of consensus between them on how to move forward. The country is divided by identity politics, culture wars, generational wealth disparity etc, you could easily be forgiven for feeling it is ungovernable.
In such circumstances, is surprising that some might yearn for an strong authoritarian leader to cut through all the different interest groups and do, on balance what is right for the majority and the country , I don't think so and history tells us we shouldn't be surprised either.
Who are these people ? Nothing sinister ,just ordinary, hard working tax payers, fucked off with paying for everything, not being listened to and being taken for granted. Are they organised and funded - no , they are just taken for granted.
No wonder the CCP are as dismissive of our version of democracy as we are of theirs.