But they aren't unreasonably preventing it.
Imposing a tax can be done for different reasons
a) to raise money. Income tax is an example. You recognise that the tax is a disincentive to something good (productivity) but you need the money for important social projects, so you minimise the disincentive whilst maximising the money raised
b) to change behaviour. There are additional taxes on alcohol and tobacco, because these impose social and financial costs. Part of the reason for the extra tax is to cover direct cost like increased NHS spending, but it's also intended to discourage people from doing it
If the government was imposing this VAT for reason (a) they could argue that they need the money, and they aren't deliberately preventing plurality of education.
But they're not.
The exact same politicians have previously attempted to ban private education (and only stopped when advised it was unlawful). This is a continuation of the same policy aim.
They've ignored economic advice that rather than raising money, this policy is likely to be net negative. They've made no attempt to analyse the economic impact of the policy because they don't care.
The purpose of this policy isn't to raise money, it's social engineering.
Nobody expects the government to make it easier for people to access private education or an expensive boarding school. Again: it's a negative right. They're not required to give it to you. They're just not permitted to prevent it or deliberately make it harder.
They are breaching the right to education when they deliberately impose taxes with the purpose of pushing people out of private education and into state.
The government's behaviour is contemptible.