Based on cursory research the British government has refuted the claim that any money is given to them from .io domain registrations.

That's an answer to a question in the House of Lords. It needs to be read between the lines. Government doesn't effectively receive anything but according to the second article cited by Wikipedia, Paul Kane, who originally runned the .io domain said that the Crown Bank was receiving money :

"In a second conversation with Kane, he reiterated that “we do remit money to the Crown bank in accordance with our agreement. We pay X amount per name.” Kane did not say what “X amount” was, due to confidentiality."

Meanwhile it seems that in 2017 Affilias has bought the .io domain for 70 millions dollars...

Well whoever's getting the money, it's not the indigenous islanders who should be getting it.

wait what?

"After being questioned as a result of the interview, the British Government denied receiving any funds from the sale of .io domain names"

So according to the linked article, no: .io names give nothing to Britain.

someone must be getting it, and it's not the islanders... so it's either the UK government, or someone they sold/gave the rights to.

Is worth noting here that the British Government denying recieving funds is not quite the same as the British Government not recieving funds.