That is incorrect.
First of all there is a starting rate of £5,000 for savers whose other income is less than £17,570 - which might apply to OP if her income is only state pension plus a small works pension.
Say someone has gross pension income of £14,000 and interest of £2,000 from a taxable account.
Their Tax Personal Allowance is £12,570. It’s used up by the first £12,570 of pension income.
The remaining £1,430 of pension income (£14,000 - £12,570) reduces the starting rate for savings by £1,430 making the starting rate for savings £3,570 (£5,000 minus £1,430).
In addition, there is the Personal Savings Allowance of £1,000 for basic rate taxpayers (£500 for 40% taxpayers, nil for 45% taxpayers). This is in addition to what can be saved in tax free ISAs. If someone has utilised their £20,000 tax free ISA allowance for the year and has other savings in taxable accounts, the first £1,000 of interest earned on them is tax free.
Adding the starting rate and Personal Savings Allowance together in this example would come to £4,470 (£3,570 + £1,000). The interest of £2,000 would be tax free.
Explained here:
www.gov.uk/apply-tax-free-interest-on-savings
and here by MoneySavingExpert Martin Lewis:
www.moneysavingexpert.com/savings/tax-free-savings/
As it seems that OP’s own pension income is less than her husband’s it might be worth considering how their savings are organised in order to take advantage of the starting rate if applicable, to put the bulk of savings in her name.
As others have said, there are easy Cash ISAs which are also flexible meaning you can take money out, and return it in the same tax year (by 5 April), without reducing your current year's ISA allowance, which is £20,000.
At the time of writing Trading 212 offer the best rates.
www.moneysavingexpert.com/savings/best-cash-isa/
Note what Lewis says in the video at around a minute in. If other income is low then you don’t necessarily need to use a cash ISA if the starting rate and Personal Savings Allowance covers the interest earned.