I tried a couple of scenarios.
1. Pension income of £55k, Interest of £5k, Cap gains of £20k, which after the 2022/23 tax free allowance is £7,700 taxable.
All £7,700 is taxed at 20%
2. Pension income of £40k, Interest of £5k, Cap gains same as above (£20k)
£5,270 is taxed at 10%
£2,430 is taxed at 20%
In scenario 2, the first £5,270 of the gain takes one to the start of the higher tax band so is taxed at the lower level.