If you work in the UK, you will have to pay Income Tax and National Insurance (NI) on your wages.
Your employer must register for PAYE and it is their responsibilty to pay your tax and NI - certainly not yours.
Be aware, that if you have a National Insurance number (you almost certainly will), the HMRC (tax people) will be tracking your payments. Failure to submit payments for a period of time will trigger an alert.
You must get a P60 at the end of every tax year and a P45 when you leave an employment.