If the last time you were in paid employment was prior to the start of the current tax year (in April), no employer would require your P45. (A P45 is just a statement of how much you've earnt and how much tax you've paid during the current tax year. At the end of the tax year it ceases to be of any importance).
The current personal allowance for income tax is �5035. You can earn up to that amount without paying any tax at all. Assuming that you have no other paid employment (and that you haven't had any other paid employment during this tax year), you could work 12 hours per week throughout the whole of the tax year, at any rate up to �8.06 per hour, without crossing this tax threshold.
National Insurance currently becomes payable when your weekly pay reaches �84. This means that, if your hourly pay is less than �7 per hour, there will be no NICs to be paid. (If your pay is higher than �7 per hour there will be a very small amount of National Insurance to be paid. Your employer shoud deduct this and also pay the corresponding employer's contribution).
As most part-time jobs for charities only offer fairly low rates of pay (i.e. you're probably on less than �7 per hour), it looks as if you'll be able to keep every penny of what you earn without worrying about tax or national insurance.
Chris