It seeks to define present-day relations between economic power and political power, the consequences for the lives of working people and the options that exist for shifting the balance of power in their favour.
The chapter begins by posing the riddle of our democracy. Workers secured the vote almost a century ago. Yet the interests of the very rich remain overwhelmingly dominant - so much so that the distribution of wealth has become even more unequal over the past 50 years.
How can this be? How can working people gain the power to elect governments, yet find that political power is still exercised against them? The answer is that there is more to power than simply governmental power. There is also state power.
This represents the whole complex of institutions that ensure that the necessary conditions are continually reproduced in which capitalist exploitation can take place.
They originated in the 17th century, when capitalist power was first consolidated in Britain.
This state power comprises all the institutions that make the unequal relationship between capital and labour inescapable and also, in terms of the way people see the world, make them seem necessary and normal.
These institutions are the legal system, the apparatus of government represented by the senior Civil Service and intelligence chiefs, the media, the education system and, in the last resort, the forces of armed coercion that defend the rights of capitalist property and prevent labour from exercising its full collective strength.
This capitalist state is far older than our democracy. It ensures that even a government wanting to move in a socialist direction is faced by a functioning system policed by market forces and an array of institutions that will seek to define and limit that government's options.
A bleak prospect, then? Yes, possibly. The past century certainly indicates as much.
But the Communist Party's programme also argues that change is possible and that the first step is to recognise the role of the capitalist state and analyse how it works concretely in present conditions.
The big problem with Labour governments has been that they have not done this. Instead, they have simply assumed that elected governments can improve the lot of working people by using parliamentary means to reform capitalism's abuses.
The communist approach put forward in BRS is quite different. Most fundamentally, it argues that socialist change can only be permanently secured by dismantling the capitalist state apparatus and replacing it through the collective power of the working class.
In the meantime, however, it insists that more limited advances can be secured in face of capitalist state power - but on two conditions.
The first is that an elected left-wing government must actively draw on the extra-parliamentary force of a mobilised working class to carry forward its democratic mandate. Only this can begin to counter-balance the concentrated power of capitalist state institutions.
The programme notes that one of the key objectives of the capitalist state in the 1920s was to get the Parliamentary Labour Party to agree that any sort of external trade union pressure on Parliament was "unconstitutional" - while that by banks and big business was totally normal and acceptable.
Previously it had always been assumed by those who fought for democracy in Britain that such electoral power had to be exercised collectively as a class, hence the very term "Labour" Party. Workers operating as isolated voters would be powerless in the face of capital. Hence the need for extra-parliamentary action to support a left agenda.
The other condition is that the combined power of the working class - economic and political - should be exercised strategically to exploit the contradictions within the capitalist state.
It is here that the new edition of BRS breaks new ground by identifying how these contradictions have changed and intensified over the past decade.
The most fundamental of these contradictions goes back a long way. It is that the modern capitalist state no longer represents the capitalist class as a whole but only the dominant monopoly section.
Early in the 20th century, a few big producers began to dominate particular markets and were thereby able to extract super-profits at the expense of other capitalists as well as workers. This had two effects. One was to depress non-monopoly profits and hence lead to deeper and more protracted economic crises.
The second was an accelerating accumulation of capital in the hands of monopoly that could not be invested internally without further intensifying crises.
The solution was for the state itself to intervene in the capitalist market - but on the terms set by the dominant groups of capital.
This intervention was both to promote external expansion - "imperialism" as Lenin described it - and increasingly to seek to manage capitalist crisis by politically redistributing income to big business to stimulate investment.
The result is what has been described as "state-monopoly capitalism."
The capitalist state increasingly operates only on behalf of a numerically small segment of the capitalist class and against the interests of the rest.
The new BRS edition details the accentuation of this process over the past decade. Super-profit is now increasingly extracted directly through the financial sector.
Investment banks use the savings of working people invested in retail banks to control and manipulate the productive economy and to divert resources, in particular, towards international speculation.
The City of London is now the world centre for these activities - with the majority of the capital US-owned.
The economically destructive consequences affect not just working people but also the great mass of small and medium firms in services and industry.
Those who benefit, the super-rich with the £4 million-plus required to invest through investment banks, constitute far less than 1 per cent of Britain's population.
Their interests enforce a system that is parasitic, dangerously dependent on an external imperialist power and which directly undermines our productive economy.
This is how the capitalist state operates in Britain today. Hence the key importance of uniting around the labour movement a much wider alliance that can expose the anti-democratic character of state-monopoly capitalism, politically isolate the ruling class and advance an alternative programme for economic regeneration and democratic transformation as envisaged by the Labour Party's early pioneers.
How to accomplish this is considered in subsequent chapters of the Communist Party's programme.
John Foster is international secretary of the Communist Party of Britain.