Change in Tax Code

Linzle1978

Hi, please could someone help me to understand this.... I'm not ashamed to admit I'm confused by it 🤯
My tax code changed at the end of November to reflect the fact that I have been working from home during the pandemic. Changing from 1250L to 1282L. I had a letter to say that this will bring a £312 tax saving for 2020/21.
Having been paid yesterday the amended tax was reflected in my wages, however, with only 5 months at the new tax bracket until the end of the financial year this will only bring me a saving of £156. I called the tax office today who told me that this is correct and not tax rebate is due as I have paid the right tax. This is the part that confuses me? If a tax code has changed halfway through a year why is it not being backdated as per the letter, and if I have paid the right tax, including the new code then does this mean that I wouldn't have paid enough on my old code? How do they work it out? 
Any help or advice greatly received 👍🏻☺️

Dazed_and_C0nfused

Why do you think it is a £312 tax saving????

It is a £312 increase in the amount you can earn before you pay tax.

Which will save you anywhere from £0 to £188 in tax.  Usually £62.40 though for most people.

molerat

Anything owed has been backdated as PAYE works out much tax is due for the whole year to date at each pay point and deducts the correct amount.  A PAYE code change from 1250 to 1282 has given you an extra £319.92 tax free for the year meaning, as a basic rate tax payer, an extra £5.33 per month in your pocket of which you would likely have received £37.33 this month.