We have PAYE - pay as you earn.
In short, I don't need to worry about my income tax - it's deducted at source based on HMRC's advised tax code.
So where I underpaid one year due to gaining private medical insurance, HMRC adjusted my tax free allowance down, so in the next tax year it all balances out.
Only tax I need to really worry about is Council Tax, but quick Direct Debit and that's sorted too.
It's all very civilised!