Sue,
I am in the same boat and only just started so it's pretty fresh in my mind!
My current employer is fine about a second job, as it is not in competition with thier business and doesn't affect my hours workign with them (if you were working all night and coming to work falling asleep I think they'd be within their rights to ask you to quit the part time! LOL!!)
You have 3 months from when you set up but then you MUST register for tax and NI within this 3 months- if you don't the fine is about £1000 I think. The number you will need to call is 0845 9154515, you will need your NI number to hand when you call and they''ll ask a couple of other questions.
Depending on your current job and how much your part time work will make, you may be able to claim small earnings exemption which means you won't have to pay NI contributions on your part time work - they will go through this with you and advise if you fall under this category. (although they said I did and would send a form but sent me a bill instead! Got it sorted no probs but had a slight panic!!LOL!).
You will need to keep a record of all your incomings and outgoings, receipts etc. You will receive a tax return each year which you will need to complete (or get an accountant to do for you) to determine how much tax you need to pay.
If you check out
www.inlandrevenue.gov.uk you can have a look at the info on there, call them or request leaflets to give you further info. I also contacted business link in my area and they've been really helpful in sedning easy to understand info and given startup advise - check out
www.businesslink.gov.uk.
If you need any more help, feel free to PM me.
B x