I'd say class in the UK is an intersection of social, cultural and economic factors.
The class system as we understand it is a post-Victorian construction that then evolved significantly with the two world wars. Historically, upper class were aristocrats and landed gentry; middle class were the professions (doctor, lawyer, dentist, academic etc.) or clergy; working class were those who were of a trade, or in manual labour etc.
This is now obviously different. For example, there are plenty of upper class (in the traditional sense) who are cash poor but asset rich; while there are plenty of traditionally working class (e.g. a plumber) who now might earn more than an early-career researcher at a university, which would traditionally be middle class.
So, it's not purely economic; nor is it purely political - working class people, for example, were fundamental to the movement for universal suffrage, the labour and union movements etc. in the same way that conservative politics have typically been the bastion of the middle and upper classes, but shifts occur.
I'd argue instead that class in the UK nowadays is about our relationship to power, and can be thought of more as a series of concentric circles than it is an up-and-down hierarchy.
Those at the centre hold the power. The circle is small, and the barriers around it are high. You need money to get there, certainly, but money isn't everything. You also need cultural capital: the right way of talking, the right way of dressing, the references to the right schools or cultural touchstones; the right connections. The central circle is small because it is beneficial to those in it for it to remain small.
The next circle out is one which is power-adjacent. It may be that a lack of money, or a lack of another type of cultural capital prevents this circle from holding power, but they benefit from a close proximity to power. These are your Hooray Henrys and I'm Alright Jacks. They are largely protected from things like the cost of living crisis because of their wealth and status, and so on.
And so it continues: it's not necessarily just three circles for upper-middle-working classes; but the further away from the centre you get, the less power and the less cultural capital you have.
Those in the periphery have the least access to power, despite being the largest group. And that's the paradox of class in the UK: the majority of people hold the minority of power.
The barriers between the levels become easier to navigate the further out from the centre you go; e.g. someone out on the periphery might move one ring further towards the centre when they have a steady income etc. but as soon as they lose their job, can't keep up with mortgage payments etc. then they're right back out at the periphery. They have no cultural capital to protect them from economic circumstances, no generational wealth to call upon etc.
I don't think Jack could ever call herself someone who's out there on the periphery. She has cultural capital in her upbringing, sure, but also in the life she's led as an adult: the connections made in being at the Groucho. The dinner parties supposedly cooking for Mary Portas. Being in a relationship with Leggy and LJC. Understanding the language of the media, being able to navigate the complexities of it. Even just being able to say "oh, this is what happens in a select committee" or "my MP pals say I should stand!"
Whatever you call it (working class/periphery/something else), I just don't think Jack can ever say that she's at the edges of power.