My own view is that the Guardian are howling in the wind with this one.
State schools and private schools are both demand led over A level choices but the difference is that state schools are demand led by students. If you don't offer the courses that students want, they will vote with their feet. Private schools are demand led by parents. If you don't offer the courses parents want they will vote with their wallets. What can you do about that?
There is no big bumper book of perfect advice. I disagree with people who say everything can be found with a little Googling. There were three pieces of advice about doing further maths A level. In a sense, all are right. The private school teacher realises grades are king. If you don't get the grades, you won't get it. The RG university doesn't insist on further maths because it knows that if you put little known or difficult to achieve barriers to entry you end up with poor students who happen by accident or design get over the barrier. The Oxbridge college doesn't have a problem with a supply of able candidates. It is looking to sniff out a less able candidate trying to paper over his weaknesses. He didn't speak to a lower ranked university but if he had that might have said "do as much maths as possible". It might not be bothered about entrance grades but that candidates with less maths drop out or fail the first year. Therefore you can have four different pieces of correct advice about the same question, depending on the perspective.
It looks like the author is essentially a middle class journalist whose kid is at a state school because he doesn't have enough money to pay the fees for London day schools. He is seeing the future through the same prism as the independent school parents but is finding that his school's response is more cloudy than theirs. In reality the life chances of his kid is probably not dissimilar to that of his independently educated peers. But what about those whose life chances are different? What he has is a belief in the universal value of an academic education and I am not sure that is right.
The state school that does not encourage someone with the ability to get to Oxbridge is disgrace. The state school that encourages the working class girl with artistic flair onto the hair and beauty course rather than A levels with a view to a history of art degree at Sheffield or de Monfort, I am not so sure about. At age 32, the graduate is an Executive Officer with Ministry of Justice. The girl with the ability to be a graduate but who did the hairdressing course has opened her own salon. Who would you say has done better? Why shouldn't the advice to the middle class girl be the same? The difference is, she is never going to go into the hairdressing business. After graduating, she might after numerous internships, get a job in a gallery or museum, but she is also quite likely to have her own business. The difference is, her business won't make any money and she will be supported by Daddy or hubby.