If you get another job, second employer will ask you to sign a form P46 to say that his is your main job. You can't do that, so he will automatically put you on code BR (Basic Rate) which means you will suffer a 20% deduction (1/5). However if you are in the 40% tax bracket, you should contact your current tax office, who will arrange for code D0 to be issued at second job.
If you do anything on a self-employed basis, you should register to get an annual Tax Return, with employment and self-employed pages. After completion, you will get a bill for extra tax, with instructions on when and how to make it. You can register on http://www.hmrc.gov.uk , and look at self-employed section.
Call HMRC and explain that you have either a second employment or you are also self-employed. Your employer would deduct tax if you are employed, or you fill in a self-assessment every year if not.
If the work in your spare time if for other companies then the tax will automatically be stopped. If it's not then contact the tax office who will send you a self assessment form.
There are lot of professionals you may seek for help. You may find on one this directory in your area if you are in London
You will be taxed using tax code 'BR' which means basic rate of 20%.