Yep, as far as I am aware, there's no mechanism by which tax can be deducted from State Pension.
If you are due to pay tax, the Inland Revenue will usually (but not always) tax the largest source of other income you have, whether it's an occupational pension like your RAF pension, or even a job if you've continued working beyond retirement, stacking shelves in Asda for example......
Where pensioners (and other folk)
are going to get caught out this year - and I'm one of them - is where in 2023/24 (the year to 05/04/24), they earned more than £500 on bank or building society interest, so on, which is paid gross and thus liable to tax. There's been a "perfect storm" of higher interest rates and the lowering of the tax-free threshold from £1,000 to the said £500.
I know how much I've earned, and I know how much tax I owe. I was going to go on-line, tell them, and ask them to re-code my occupational pension accordingly. But all the advice from HMR&C is "don't call us, we'll tell you once the banks etc. have notified us independently of your income". Right, so I'm not bothering, then. I'll wait and see what sort of figure they come up with when I get an amended code - and I'll lay you a tenner it won't be anywhere near correct .....
I'll then have to start trying to get them to put it right. Lay you another tenner that won't be resolved this side of next April .... by which time we'll be in another tax year!