Working out tax on second job - please help!

your first job uses up all of your personal tax free allowance of £11,500 so anything you earn in the second job gets taxed at 20%. However NI works differently and you still get the first £157 per week without any NI deduction

No idea what is a realistic pension contribution, but sticking with the 3% mentioned above

if gross pay is £15.25 per hour for 20 hours = £305.00 per week
3% pension on that = £9.15
taxable pay therefore 305 - 9.15 = 295.85
income tax on 295.85 @ 20% = 59.17
NI on 295.85 - 157 = 138.85 @ 12% = 16.66

take home pay per week 305 - 9.15 - 59.17 - 16.66 = 220.02

220.02/20 hours = £11.00 per hour net pay post tax

I appreciate you may not think in terms of annual salary but for a 40 hour week £15.25 gross per hour is equivalent to an annual salary of £31,720

obviously if the pension % is different (it can't be less than 1%) the above will change, but it may be easier to tell prospective employers you want at least £300 per week before tax

so you understand fully, note that in your current (first) job the fact your income tax personal allowance is available to that means the first £221.15 (11,500/52) is free of income tax. So, depending on how much the pension % is, your current employers are paying you very little more than £11 per hour. For example if the pension is 1% then the gross cost to them would be £11.11 per hr (£222 per week) not £15.25!!! So think carefully about whether you can sell yourself to the same sort of potential employers given you need £300+ per week rather than £222 per week.