Here, in sunny Norfolk, most of the DD council tax payers got their money into their bank accounts by the end of May. Letters were sent to everyone else with a 1 time password on them. Seemed to work, mostly.
Some people had to send statements (and moaned about it) because there are prepayment assurance checks made to the bank accounts via a bit of government software. Not all banks subscribe to the govt software, which is why the local authorities ask for a statement showing name, address, sort code and account number. Many of the online only banks don't have the checking agreement and one or two of the big high street banks.
Joint accounts stuff things up because, in general, letters are sent to the first named person on the Council Tax bill. No idea why.
The checks are in place so that unscrupulous people cannot pinch their parents/aged aunts/grandparents rebate money. The local authorities will be audited on the payments, as will the cabinet office.
Pretty sure that the council tax department, up and down the country, found out that the payments were being administered by them at the same time the general public did.
People who don’t have bank accounts have the option to credit their council tax bill, some councils are sending cheques, some send prepaid visa cards. Everyone who is entitled should get paid. The money comes from the cabinet office, not the councils. The staff are doing their best.