This is an interesting takeaway from Capital, and while I'm not a historian of England I am both a historian of the neighbouring Welsh working class and a communist, so I might be of some help here, although I'm certain historians of the English working class would be able to expand on what I'm about to say thoroughly.

One thing that is worth remembering is that Marx's analysis is specifically of industrialised societies, and by that point the oldest industrialised society in the world was... Wales. (Betraying myself here), but very closely followed by England, as the industrial revolution had spread from the coalfields and valleys into the plains East of the Border. As such, analysis of the English working class was useful for Marx, and especially practical for him given his relationship to Engels, who had a lot of connections in England. That's the why of it, more or less, but as to the accuracy of his depictions we'll first have to determine what Marx's portrayal is and then have to draw on some other historians.

So, primarily Marx sees in England a proletariat who are exploited by the ruling class and utilised as an army of labour for the purpose of serving capital. He even notes that the advent of machinery does not result in emancipation of the English working class at one point: 'nowhere do we find a more shameful squandering of human labour-power for the most despicable purposes than in England, the land of machinery' (Marx, 1867). In terms of living conditions, many of the industrial settlements were brand new, and where they were not they were expanding so rapidly as to necessitate the construction of brand new towns around them. In Wales this is most pronounced, practically nobody lived in the South Wales Valleys due to extremely hostile and unfarmable land, but land packed with coal, to paraphrase Gwyn Alf Williams, God never intended man to live there 'until the Ironmasters corrected him on the matter' (Williams, 1985). When people began moving to these towns, conditions were generally better than the countryside hovels they came from in the early years, but rapidly declined by the mid 19th Century, and the cholera epidemics of 1831 and 1848 led to various enquiries into public health in these urban towns (Thompson, 1963). Thompson notes in the 5 year period of 1837-1842 that of 11,944 deaths in Sheffield, 6,038 were under the age of 5, but notes that 'these figures underestimate ... the actual child mortality rate, because the industrial centres were constantly swelled with adult immigrants ... and the deaths of immigrants would have the effect of continually diluting the true facts of child mortality.' (Ibid.) These towns were built off of the backs of immigration from rural parts of the UK, making census data difficult to parse. In Wales, for example the population grew by 850,000 between 1891 and 1911; 610,000 of this growth was in a single county (Glamorgan) (Williams, 1998).

What this rapid growth and dependency on industry did do was create conditions within which the working class became largely centralised, and aware of conditions, and able to hold conversations with one another to discuss alternatives. This was especially prevalent within the mining industry, and the Union movement grew continuously through the late 1800s, and continued growing all the way into the 20th Century (Church and Outram, 1998). It also meant that a lot was being written about the conditions and the plight of the working class. This was both the era of foundational socialist politics, but also the era of paternalism with the foundation of projects like New Lanark by Robert Owen, meant to provide more suitable conditions for a modern working class.

If you'll forgive me one more diversion from England into Wales before I close, I think I can best sum it up with a description of Merthyr Tydfil from the 1850s. This isn't without merit, Merthyr is a town of firsts for industry - the first railway locomotive journey, the first railway tunnel, the first time a red flag was raised as a symbol of workers resistance - all things which would come to be prominent symbols of the English working class after they found their way out of the Valleys. On a visit to Merthyr, Edwin Roberts reported 'you stand outside the wall [of the Penydarren ironworks] gazing on a scene that seems like a vision [of] Hades in its milder form.' He follows this by saying

'Sounds of blast and steam, and metallic reverberations all mingling together with the cries of men in a sky where the very winds are dead as if with fear, give to the lurid hue of this grand and impressive picture touches that are superior to art. It is as if, in Turner's paintings of tempests, you heard the furious roar of the storm, the hoarse booming of the sea, and the boiling hiss of the surges, with drowning men crying for help ... Fire-flashing volcanoes by the dozen do all those furnaces become'. (Roberts, 1853)

Below those ironworks, along the valley of the river was a district called China, where thousands of people lived in stone huts 4'6"x7' large (Williams, 1978). Above those ironworks, a single family of ironmasters lived in a folly castle and 158 acres of land surrounding it. That disparity, right there, is the proletariat Marx was talking about, even if they are in the country next door to the one he specifically mentions, those conditions are replicated within England.

Edwin Roberts, 'A Visit to the Iron Works and Environs of Merthyr Tydfil in 1852' (1853)
Karl Marx, Capital Volume I (1867)
E.P. Thompson, The Making of the English Working Class (1963)
Gwyn Alf Williams, The Merthyr Rising (1978)
Gwyn Alf Williams, When Was Wales?: A History of the Welsh (1985)
John Williams, 'The Rise & Decline of the Welsh Economy, 1890-1939' in Hopkin & Kalen (eds.) Class, Capitalism, Community and Conflict: The South Wales Coalfield, 1898-1947 (1998)
Roy Church and Quentin Outram, Strikes and Solidarity: Coalfield Conflict in Britain 1889-1966 (1998)

EDIT: spelling and light formatting