£500K starting Private School Fund - sufficient?

[Account18]

We have 2 sons who will start in pre-prep over the next 2 years.

In today’s money:

• We have savings/investments of £500K set aside for this purpose
• Local school fees are roughly £15K for primary / £30K for secondary (excluding extras)

Question:
Would this be sufficient to pay for private schooling over the next ~16 years?
My assumption is that both the investments and the fees will increase over time, but trying to sense check whether the starting pot is broadly in the right ballpark.

I’d be interested in both:

• Anecdotal experiences from those who’ve done something similar
• Quantitative views on whether the maths broadly works

Note:
This is a separate pot specifically earmarked for school fees (separate from pensions, housing, inheritance, etc). Our pensions are on track, housing costs are covered by income, and there may be some early inheritance available if needed (though we’re not assuming that). We also have some excess income each year that could contribute if required.

Trying to gauge whether £500K feels sensible/optimistic/cautious

Thank you

There is more to think about than whether they will have a high paying career. There is the educational experience, the person they will become, the friends they may make for life and whether they will enjoy their school years.

I was horribly bullied at the private school I attended, hated it, and don't keep in touch with any friends. I appreciate others have had better experiences though.