Tax to be paid in excess of £1000 tax allowance.

To be clear, is this tax demand purely on interest from savings? Or, could some of it be because his other income has risen, if his State Pension now exceeds the Personal Allowance?
Has HMRC sent a breakdown of the figures?
I take it your DH does not do self assessment? So this will be based on figures HMRC have received from employers, pension funds, DWP for State Pension, banks and building societies etc.
If the extra tax is based on interest, then he needs to inform HMRC that these are joint accounts, and get the interest allocated appropriately.

Firstly, I think it depends why you have to complete a tax return in the first place.
I did my mine (I have a rental house, so I’m classed for self assessment) before Xmas and it came back as expected, but there’s a new system in place, known as Advance Payment, so as well as what I thought I’d owe, I’ve to pay a further 50% of that figure by the end of this month. An example would be, if I owe £1K, I’ve to pay £1500 in January and a further £500 in July. The advance amount is based on what my income is expected to be for 24/25.

The theory is that I’ve had the income from 23/24 and would normally not pay any tax until 25, whereas those receiving pensions/other income are paying their tax as they receive their income.

Does that make sense? Is your demand literally half as much again as you were expecting?
Look up HMRC Advance Payments - it explained it all to me.

Our tax liabilities on savings are for each of us, as we have the savings in separate accounts, for us it makes tax sense.
I once asked the bank, some years ago, about tax on a joint account and they said it depended on whose name was first on the account. Thus DH was deemed ‘in charge’ of the account.
Maybe it’s the same now, but might have changed.

I can only tell you what someone at the tax office told me when I rang once about DH’s tax code number.

She said they couldn’t tell if savings were in joint or sole accounts, she took note of what I told her, which accounts were which.

It seemed that the banks/building societies just forwarded the interest amounts without designating if they were sole or joint.

If anyone knows different, I would be interested to hear.