For the first half of the 20th century, the democratic Left was associated with socialised services, economic regulation, high wages and worker's rights,, while the Right espoused militarism, privatised services, free markets and low wages. The 1960s counterculture crucially changed the beliefs of the so called New Left in the direction of pacifism, minority rights and social libertarianism, and these positions have now merged into the mainstream Left to produce a bewildering range of different combinations and sects.
The Right still likes militarism, free markets, and individualism but has also adopted substantial parts of New Left libertarianism, to further complicate things. Apropos of which, this disturbing and highly unorthodox blog post by Dale Beran may come as a surprise if you're unfamiliar with the seamy end of the Internet: https://medium.com/@DaleBeran/
What's happened is that major changes in the economy - financialisation, falling profit rates, neoliberal fiscal policies - have reduced the Left's ability to deliver social democracy, and as a consequence the generation of the 1960s' counterculture, (that is, mine) substituted a new position based on anti-racism, LGBT rights, and much more - what's often called 'identity politics' but could equally be called 'minoritarianism' . Sometimes this switch is justified by reference to Gramsci's concept of hegemony, that is achieving power over culture and society in times when state power is unattainable. (In fact he still saw state-power as the ultimate goal)
An insightful article in the LRB by UCL's professor of Philosophy of Law, George Letsas (https://www.lrb.co.uk/v39/n06/george-letsas/brexit-and-the-constitution) shows a different way to see what's actually happened. He criticises the usual definition of that 'populism' which lead to Brexit and Trump's victory, namely that it means bowing to 'what the people want' and deploying rhetoric that appeals to their emotions. Instead he attacks this populism in politico-legal terms, as a 'deliberate attempt to bypass the normal channels of representative democracy'. That might sound like the same thing, but it isn't.
Rather than 'populism' this approach is better called 'majoritarianism'. It claims that the sole justification for political action is indeed 'what the people want', but more precisely, what they voted for in the last election or referendum. This conception of democracy is held by as many on the Left as on the Right (of those who adhere to democracy at all that is), but it doesn't correspond to the way UK democracy, or many others, actually work. Democratic political action was until recently always justified by a continual process of collaboration and conflict between the executive, legislature and electorate - the process we call 'checks and balances' - which, however imperfectly, protects at least some of the rights of the minorities within the majority.
This creeping majoritarianism in the wake of Brexit and Trump isn't yet the full-scale authoritarianism or fascism that some on the more excitable Left are claiming, but it is their precondition. It's also clear that the so-called Alt-Right is fully aware of the crucial role such checks-and-balances play in maintaining liberal forms of democracy, and they're rapidly achieving sufficient power to undo them all. And one reason that such majoritarianism is gaining popular support so rapidly is precisely the fact that the Left has more or less given itself over to minoritarianism.
Of course the mass media play an important role in encouraging majoritarianism, but they merely complete a vicious circle with the Left's increasingly extreme and vociferous minoritarianism. The still-mostly-silent majority believes that its interests are being sacrificed to those of a wide range of minorities, in a process that inexorably inflates rather than combats racism, sexism, xenophobia and the rest of the isms.
This almost universal misconception about the nature of representative democracy renders 'more democratic than thou' political arguments moot, as the rancour over Brexit so clearly demonstrates. Letsas doesn't claim that understanding it will solve the problems of the Left, far from it. Particularly among younger people, confusion caused by the New Right's espousal of libertarianism, 'anti-elitism' and anti-PC runs deep, and any policy solutions for the Left aren't at all obvious. Letsas does suggest that in the long-term one way out is a written constitution for the UK, something I've always believed to be less important than electoral reform, but I think he has convinced me.