One of the good things about UK taxes is that you don’t have to calculate them yourself and file a return. They are calculated by your employer and deducted from your salary.
Also if you pass a certain income threshold you're required to fill in your own tax return anyway.
That is correct. However, HMRC sends you a letter with every tax code change, which is calculated and posted automatically; I've once received two separate letters, with two different tax codes, sent literally one day apart from each other. :D
And if you feel that you tax code is incorrect it is very easy to check your online HNRC account and correct any information they might have.