The way I see it, populism can be used to describe two things:
A popular backlash when the establishment of a society starts using their institutional powers in a way that is anathema to popular wishes, leading to a revolt against the establishment by people.
A systematic distrust of elites and establishment, with trust placed instead in the ordinary people at the bottom of the pyramid, under the view that those who live with the consequences of social decisions are better placed to understand their ramifications and to choose better paths.
What Piers Morgan describes is the first type of populism. The reality is that progressives have over time taken over most political and social institutions. Whether that was conscious (long walk through the institutions) or not is not that important in the end, the result is the same. Academia is the gate-keeper of the establishment in Western societies, as positions of institutional power usually require degrees and networking enabled through the academy. As academia became more and more progressive, all establishment institutions downstream from it (civil service, the judiciary, public and private administration, the education system, the media, etc...) started also turning more and more progressive. The result is that progressive rhetoric has become dominant and the establishment keeps pushing progressive policies that are often at odds with what most people think, creating the sentiment of abrasive "political correctness".
Now, people have a certain degree of tolerance for the establishment acting in ways they dislike. Taking a stand against policies they dislike has a cost, and many may choose to tolerate the indignity in order to minimize disturbances to their personal lives. But when people have enough, and someone comes along who is willing to push back, taking aim at the establishment, then you have the conditions for a populist backlash on your hands.
FTR, when I say "establishment", I mean people who hold stable positions of influence within social institutions that are able to influence and shape society's evolution. They can be university professors or administration, major civil servants, major media, judges, influential members of political parties (whether they're elected or not, but they must be long-term fixtures with influence), etc...
Anyway, a typical criticism of "populists" is that they don't attack the existence of elites/the establishment, they simply want to be in it. That's not entirely wrong, but neither is that necessarily hypocritical. In the case of a "populist backlash", the system is not always attacked directly, instead, the "populists" are generally saying that the system is being perverted and misused by those currently in power in the institutions, and that what is wrong with it can be fixed by replacing the current crop of arrogant and out of touch "elites" by new "elites" who are more in touch of the population, more respectful of it and who will use their power in a more responsible manner.
It's not that different from the "loyal opposition" party in a democracy... this is a party that is not opposed to the political system, they are loyal to the system, they just think the people running things within that system are making a pig's mess of things and are arguing for being put in their place.
An ideological populist on the other hand would argue that the problem isn't just the current group of elites, the system itself is at fault. It doesn't suffice to remove the current elites, the establishment's power must be curtailed and subjected to popular opinion far, far more. For instance, an ideological populist would favor elected judges, elected police chiefs, strict term limits for politicians, local control of schools and universities, breaking up big media companies for the sake of local media, etc, etc... This would signify a systematic distrust of any kind of establishment, and the desire to break up and destabilize any institution to reduce their power and influence.
I think we saw this rebellion happen on the Left in the 60's through the 80's until they wrested control of these various institutions, imo, organically.
What we're seeing now is a similar, but weirdly absurdist, revolt by the masses against Liberals (or whatever you want to call them). It seems much more chaotic and disenfranchised than what we saw from the Leftists. They at least believed in the institutions in that they could serve as vehicles to benefit the masses. However, the 'tune in, drop out' mantra isn't a new one and we can see this is a theme for a good percentage of the population during any given era; they just have 4chan now rather than vinyl records to spread the message.