I was trying to figure out where you got 1257 from, presumable your tax code? @Kim has explained it well. Only addition from me is complexity around taxable benefits or earning over £100k which reduces your tax free allowance.
@Kim thank you. That explains everything
No, everyone gets £12570 tax free per year but if you are paid monthly then it is equally split allocated to £1047.50. If your gross pay is £1262, you will essentially pay tax on the £214.50 that your over the threshold. (Works out about £42 tax to pay)