You can find a lot of information at the HRMC website at http://hmrc.gov.uk.
If you don't want to work as an employee, you can register as self-employed (basically a one-man band), which is quite simple, you can start your own company, which is more work but can have tax advantages, or you can find umbrella companies which will officially employ you while in reality you are a freelancer and only do your billing through them.
Umbrella companies can be anywhere from totally legal to extremely dodgy. If they promise you that you pay only five percent tax on your income through ingenious tricks, that's only until the tax office finds out and they will make you pay.
Between self-employed and your own company, the big difference is whether you are actually working independently or not. If you work like an employee (take someone else's orders) and claim you are a company, the tax office doesn't like that. And if you pay very little taxes, they don't like that either. So self-employed is the safer choice but you will pay more taxes, close to what a normal employee would pay.
Obviously you will have to pay tax on your income and NHS insurance.
Obviously you are required to tell the government (actually HMRC) about your income. Not doing so would be tax evasion and get you into deep trouble when you are caught.
I don't think you have to tell them the source of your income, but not telling them might look very suspicious and might get your accounts checked carefully. And unless you design a website for the mafia, why wouldn't you tell them? The bill payer will try to deduct your bill from their profits anyway, so it's no secret.
Most important to remember: When you send out a bill and receive payment, you'll have to pay tax on it. When self employed, as a rule of thumb put one third away into a savings account for your tax bill. Don't spend it all or you will find yourself in deep trouble when your taxes need paying. Plus put some more away for times when you can't find work.