For the vast majority of people in the UK, you're allowed to earn �6475 in the current year without paying tax on it. That's equivalent to �124.52 per week, or �498.08 per 4-week period.
So, if your gross pay for a 4-week period is, say, �1000, you'll pay tax on �501.20.
Tax (for those who don't fall into the higher tax band) is charged at 20%. (So you'll be left with 80% of your taxable income).
So, to work out your net pay, subtract �498.08 from your gross pay. (To get your taxable income). Then multiply by 0.8 (to knock off the tax). Then add the �498.08 back on again.
At least that's theoretically how you could do it. But that method will actually only work if you earn the SAME amount during each 4-week period. The 'real' calculation (which is needed if your 4-weekly income varies) is far more complicated:
1. Add your gross income, for the 4-week period, to your previous total gross income (since the start of the current tax year)
2. Multiply the number of weeks, so far, in the current tax year by �124.52.
3. Subtract the figure from paragraph 2 from that in paragraph 1. (That will give your total taxable pay so far this tax year)
4. Multiply the figure from paragraph 3 by 0.2 (to find out how much tax you should have paid up to now).
5. Subtract the total amount of tax you've already paid, in the current tax year, from the figure from paragraph 4. (That will tell you how much you now have to pay).
6. Subtract the figure from paragraph 5 from your gross pay for the 4 week period.
NB: Nothing in either method takes into account National Insurance!
Chris