What I'm getting stuck on is the payments on account as these aren't calculated on the tax due calculation
Your January 2022 payment will be the tax due for 20/21 minus any payments on account you have already made plus your first payment on account for 21/22. So, if your total due on the calculation says £5k and you've already paid £3k, then you have a balancing payment of £2k plus a payment on account of £2.5k, total £4.5k. If you're filing now, they will send you a statement before January showing what's due.
Your January 2022 payment will be the tax due for 20/21 minus any payments on account you have already made plus your first payment on account for 21/22. So, if your total due on the calculation says £5k and you've already paid £3k, then you have a balancing payment of £2k plus a payment on account of £2.5k, total £4.5k. If you're filing now, they will send you a statement before January showing what's due.