These are extremely distinct and an arbitrary assortment of people, with no real business being grouped together in a meanignfull class analysis.

That's the point in the middle class. They are a mixture of people who are too well off for being placed proletarian status, but not enough to be within the petite bourgeoisie. They share a class culture in their values of aspiration and such. The used car salesmen want a bigger better trading platform. The small business owner wants to build up their business. The intelligentsia are not proletariat. They're not. Sometimes they are actually counted as their own class (to be honest one could make the argument that academia is its own microcosm, but that's neither here nor there), but they are not proletariat. Neither are they bourgeoisie.

You are using terms you do not understand

My a-level in sociology says otherwise. Do not insult my intelligence again.

The term proletarian is closely associated with physical work

So builders and plumbers are not physical? Blimey, best tell various members of my family that, then.

but the analysis itself cares not for superficial nature of the work, because, again, that's arbitrary and says nothing about societal relations

So Working Men's Clubs, Miners' Welfares, pub culture, canteen culture - none of these exist or have existed?

Again with you saturday morning-cartoon understanding of Communists

Do not insult my intelligence again. Communism is based within class warfare - that the two classes hate each other and are in conflict.

They run most of the economy

It is often said that small businesses form the backbone of the British economy.

eight hours or more of most people's days

Depending upon their contracts.

they run public perception

It is not a secret society, you know.

they run media

Explain the publicly owned BBC who hold a media monopoly.

regardless of whatever laws in place - they still manage to uphold their interest with the state!

Well done! You've worked out that the Government are statists! Who'd have thought?

An actually meaningful class analysis is one that delves into what societal interests is held inherently with what people - what material position do we have in society in regards for eachother. Importantly, how do these interests contradict eachother and how does that take expression in society?

See above.

You either own the factories. or you work in them

Thus is the fundamental problem of Marxism. This is not the nineteenth century, and Britain has not been an industrial landscape for many years. Many jobs which were middle class are now considered working class. Office work is a good example of this.

And, in other word, proletarians. (Regarding the use of "proletarian" to mean only physical work)

And the non-physical worker? They certainly aren't lumpen proletariat, after all as they are useful to society.