I used to do the books for my partner - not an expert but..
Basically you would be on BR (basic rate) and would get no tax allowance on your second job - approx 22% of everything you earned in that job would be taken in tax. You would also, if you earned more than approx £100, have to pay National Insurance.
I'm pretty sure that there is some thing where you can pay less NI but not sure how it works...or the sums would be worth your while.
Or how it would work if you were in the higher (40%)tax bracket for your primary job -ie earn over approx £35K pa.
Best to give HM customs and revenue a call - they have a brilliant employers helpline but can't find similar for employees..call any dept (from the phone book) and they will point you in the right direction...