There's no such thing as a tax free allowance any more. It works like this:
All of your income is taxed, first at 20%, then at 41% if you earn enough.
This gives a notional amount of tax. E.g if you earn 20k you would have notional tax at 20%, of 4k.
You then take your tax credit away from this notional figure to arrive at the actual amount of tax payable. So in my example, if you are a single PAYE worker you will have 3,300 of tax credit, so you subtract this from the notional tax of 4k, so you should pay 700 in tax.
So to answer your question, as a rule of thumb the amount you can earn before paying tax, is approximately 5 times your tax credits.