People are often pointing out the problems and unfairness in the tax system. It’s like the child benefit system penalising single income households. Referring to your specific point though, this article is interesting and refutes this claim. It is, interestingly, published by the IFS (the same organisation which issued the report into VAT on school fees and an organisation which supporters of the VAT policy assure us is entirely accurate). It’s an old report but the same ideas apply. https://ifs.org.uk/articles/do-poorest-really-pay-most-tax
There is absolutely no logic in introducing a tax system which penalises education and treats cake more favourably. As far as I’m aware, no other country in the world penalises education in the same way. There is good reason for this; most people with even a tiny understanding of economics realise that education is a societal benefit. Some countries actually subsidise private schools by giving funds directly to them because they appreciate the value of a great education.
What would be interesting is if the IFS could do a report into how much VAT would be raised by adding VAT onto cake. I suspect the Labour Party don’t think that taxing Jaffa Cakes will be a similar populist vote winner.