One of my earliest televisual memories is of Derek Griffiths singing “There’s a hole in my bucket”, presumably in cahoots with a female singer and presumably on Play School although my memory is unable to fill in those blanks.

The song, if I may remind you, tells of how Henry finds a hole in his bucket and goes to his friend (Sister? Carer?) Liza to ask for advice. Unfortunately, every suggestion she provides gives rise to a new problem until we return to the beginning (having needed, at some point, to fetch water) with Henry once more complaining of a leaky bucket.

A full psychological investigation into the motives and mental state of both Liza and Henry is a niche waiting to be filled (my personal, and rather revisionist, view is that Henry is an excellent logician who has seen through the complete chain of reasoning and that Liza is an infuriating, computer-says-no, bucket insurance clerk).

Whatever the backstory, the sad tale of Liza and Henry is reflected in the situation in state sixth forms this year. The song would go something like this (please sing along, and I apologise that the scansion of some of the verses is less felicitous than the original).

“State students don’t get into Oxbridge, dear Liza, dear Liza.”

“Then teach them better - dear Henry, dear Henry.”

“But sixth form funding is inadequate, dear Liza, dear Liza”

“Then increase it, dear Henry! Dear Henry!”

“But if it’s increased then schools will spend it on fripperies while their sixth formers slouch around the place and pollute the atmosphere of the bike sheds. Dear Liza, dear Liza.”

“Then check that they don’t when you inspect them. Dear Henry, dear Henry.”

“But inspectors are focused on GCSE and barely look at sixth-forms which are notoriously hard to compare anyway, dear Liza, dear Liza.”

“Then get better inspectors, dear Henry, dear Henry.”

I’m abandoning my extended bucket analogy here because this is no music-hall act with a circular ending, a pratfall and a round of applause. This is real life chances for our young people during two crucial years - the two years that they spend between the uniform curriculum of GCSEs and the post-18 free-for-all of universities, college, employment, apprenticeships or an alternative. We have to take these years seriously - and that means funding them seriously.

At the moment, government funding is based around 540 guided learning hours (time in classrooms) each year. In a 40-week year that’s less than 14 hours a week. No employer thinks that’s full time so why are we telling our impressionable teenagers that working beyond that is basically optional? It costs about a thousand pounds per student above government funding to get up to the 20+ hours a week of teaching that private schools provide and so back of the envelope calculations suggest that it would cost £2 billion a year to fill this hole.

That’s a lot of money and, as our friend Henry pointed out, we don’t have a good system for checking that it would be spent properly and easy answers, as Liza has shown, are no good. But, unless we find a way of fixing this hole in the sixth form funding we will continue to go round in circles over access to top universities and top jobs and, worse than that, we will continue to do our young people (and hence our future) a disservice.

It is simply not reasonable to expect disadvantaged young people to compete with peers who, as well as houses full of books, access to a wide range of cultural experiences, and small classes have had 50 per cent more teaching every week through their sixth form.

There’s a hole in my bucket.

James Handscombe is the principal of Harris Westminster Sixth Form. He tweets @JamesHandscombe