As I understand it, 437L means you are allowed to earn �4,370 before paying any tax. 503L means you get �5,030 tax free. In other words, you only pay tax on earnings over those amounts.
The only odd thing is that 437L was not the standard code for last year - I assume you were paying off arrears of tax from an earlier year? If not, I suggest you check why it was different.
dzug, no need to scare poor old linzi, it might just be down to the simple fact that Linizi may have a pension, personal health care, company car, fuel card etc etc all taxable items and perks which affect your tax code. Linzi speak to your accounts dept, person who does your wages, and speak to you local tax office if you are worried. My tax code was 489L, and is now 503L also meaning that you can earn �5030 before tax is deductable.
The personal allowance this year is �5,035 (last year it was �4,895). Money earned above this sum is taxable. It will attract Income Tax at 10% for the first �2,150, at 22% for taxable amounts between �2,151 and �33,300 and at 40% on taxable amounts over �33,300.