After income tax it leaves about £3,400 a month. Rent or a mortgage, council tax, energy and food will take the vast majority of that, making it very hard to build wealth and get ahead - even without kids in the mix.
I think a lot of people on comfortable incomes have absolutely no idea how privileged they are.
I also know people who complain about their financial situation in the same breath that they contemplate spending £15K/year or more per child on private education, in spite of having good state schools available.
[1] https://ifs.org.uk/tools_and_resources/where_do_you_fit_in
That is before taxes and redistribution though. People without income or with _de minimis_ income would get their housing cost paid (which costs £20k-£30k per year in London, i.e. 25-40k of pre-tax salary), their council tax bill paid, their TV licence fee waived, prescription and dentistry fees waived, childcare subsidised, and would get £400 of spending money per person on top for bills, food etc.
Which is why people on zero income in London can afford to have 2-3 kids, but two people on £50k combined income cannot.
Generally speaking it all starts when you're young. The best is having poor/tight parents. The worst that can happen is you get a poorly paying job yourself and consider this normal. But there's a strong chance you'll get a better paying job and not ever have to worry about money. The worst is having middle class parents who spend their money. Now even if you get a job as well paying, which isn't guaranteed, you'll simply have what you think is normal. But there's a strong chance you'll get a worse paying job and always struggle with money.
If we're talking a mortgage it won't take the majority of that. Most people are paying no more than a couple of hundred in interest on their mortgage, many pay much less. The repayments aren't "taken", they are yours and are paying back the loan on the house. In other words, they are building wealth.
It's rent and consumption driven by lifestyle inflation that traps people in a cycle of not building any wealth. Mortgages are for the wealth-building class and are therefore a good deal.
So, yeah, earning £60k isn't what makes you middle class any more. It all depends on whether you own a house or not.