Personally find the concept of 'patriarchy', when applied to liberal western societies, pretty defunct and also problematical. I used to use it when younger, but I reject it now.
Patriarchy, strictly speaking, is the rule of the father, or by men more generally - in which women and girls are seen as the property of their father, and where women and girls do not have equal rights in law. There are certainly many societies in which patriarchy is most definitely still a thing. Afghanistan is probably one of the most extreme versions of the patriarchy.
I personally don't think that 'patriarchy' applies to us in the West anymore....... what we are left with is general differences between the sexes. Physical and biological differences and all that stems from those differences. I think raging against these differnces is pretty pointless and ultimately doesn't change them, either.
Unless we envisage a future in which babies are gestated outside of the body and brought up in state run establishments ( communism has come pretty close to this vision in certain ways - in which the state takes on a totalitarian character) then women ( in general) will always tend to carry the biggest share of childcare and domestic responsibility. Obviously, some families, happily and easily, make other arrangements along more equitable lines......but for many these issues tend to be one of the prime reasons for marital or relationship breakdown.
Women are increasingly having to do everything......have children and the related domestic responsibilities, but also a full time career, and lifestyles have become predicated on two full time incomes. so even if a woman wants to take a few years off, or go down to P/T she is unable to. Some women are putting off, or not having children at all. I'm not sure this is becauase of 'patriarchy' though - it is far more practical than that.
After all these years of feminism we still see male violence and sexual assaults - and i don't think that will ever change. Males are simply more predisposed to violent and sexual crime.....although, of course, not all men are violent or are rapists. Holding all men responsible for the behaviour of some men is not a winning game in my view, and doing this just makes women feel permanently angry.
Gregg Wallace is an example of a sex obsessed, probably porn addicted, man and he's definitely not the only one. But I don't see his behaviour as being down to 'patriarchy'. I think his behaviour is a result of his own male role models, his own character and his own life experiences - combined with natural heterosexual male tendencies. He alone has to take responsibility for his behaviour. John Torode managed to conduct himslef in a respectful way towards his female colleagues.
I recall when Reading Andrea Dworkin - who most certainly suffered terribly at the hands of men - I'd come away feeling absolute rage and hatred towards men......though I'm also sure that is not a healthy state to be in. Her experiences were extreme, and there are definitely some women who have suffered similarly...but not most of us.
In short, I'm more accepting of sex based differences now and have reconciled myself with them. And as such, i don't recognise British society as a patriarchal one. The reason we have singles sex spaces, services and sports, for example....is in recognition of some of the differences between the sexes - not because women as a group are oppressed. We have such safeguarding rules and they are based both on predictable risks and out of a sense of female dignity and worth.
Mary Harrington is a thinker who I have a lot of time for on this area of thought...though at times she can be a little too esoteric, with her own self created vocabulary and concepts.....but interesting nonetheless, and willing to psuh the boundaries of thinking when it comes to contemporary society and the positions of men and women in it.