Call it what you want, it's income tax

Worse that that it’s a tax on earned income i.e. people working, so landlords etc don’t pay it on their unearned income i.e. rents

No, they definitely pay income tax on rent. HMRC deducts any rental income from your tax free allowance on income ahead of time in fact.

They were referring to National Insurance, not Income Tax

Apart from applying in a different range of circumstances and being capped, yes it's linked to income.

(Does raise the question of whether student loan repayments, which are also linked to income unlike other loans, and have been called a "graduate tax" by some of their advocates, are also an income tax that applies only to people born after a particular date ...)

They're only an income tax if you can't pay them off. Call it a tax on the poor and normal, while as ever the wealthier cohorts get a nice break. This is why there should have been an actual graduate tax.

That and the fact that a graduate tax would at least have been predictable, unlike, say, the soaring interest rates on student debt at the moment.

No it doesn't, it is just another income tax.