To fill in a bit of detail on what's already been written (and using weekly pay, rather than monthly, for my example):
You're allowed to earn £8105 without paying tax in the current tax year. That's roughly £156 per week.
So, at the end of the first week of the tax year the tax man deducts £156 from your earnings (or other relevant income) and takes 20% of what's left.
At the end of the second week he takes £312 (i.e two lots of £156) from your TOTAL earnings across the TWO weeks and calculates 20% of what's left. That's the TOTAL amount of tax which you should have paid, so he knocks off what you'd paid in the first week and charges you the rest.
At the end of the third week he takes £468 (i.e. three lots of £156) from your TOTAL earnings across the THREE weeks and calculates 20% of what's left. That's the TOTAL amount of tax which you should have paid up until the end of Week 3, so knocks of what you'd paid up by the end of Week 2 and charges you the rest.
That process continues week by week. So your first pay statement will be about 22 weeks into the year. The tax man will then look at your TOTAL income (from both JSA and your new employment) up until then and knock off 22 lots of £156 (= £3432) to work out the TOTAL amount of TAXABLE income you've accrued over the year. Unless you've just landed a really fantastic job (paying thousands of pounds per week) the figure he gets will be negative, so you won't have to pay any tax on your first pay packet.
As time goes by your TOTAL pay for the tax year to date will gradually catch up with your tax free allowance (in multiples of £156) at that point, so you'll start paying tax. However if you're earning less than about £218 per week you won't actually reach the threshold within the current tax year (which ends on 5th April). Even with pay of £300 per week it would be around 3 months before your total pay would catch up with your allowance.
Chris