"As an assumption your state pension will take up more or less all of your free pay allowance (£10k this year),"
Not quite. The basic State Pension is currently £113.10 per week (£5881 per annum). When you receive your State pension, because it forms part of your taxable pay but is paid free of tax your tax code (which for most people this year is 1000, representing £10,000 tax free allowance) will be reduced by your state pension sum (588, representing £5,881 if you receive the current maximum basic pension). This will make your tax code 412, meaning you can have £4,120 extra income before you pay tax. You can have this split between, say, an employer (if you are still working) and an occupational pension provider, or more than one pension provider. You need to tell HMRC how you want your code split but once you've done so they usually adjust each of your codes as the allowance changes each year.
It is fairly straightforward but you need to keep on top of it to ensure you pay the correct tax.