In short the answer to that is yes, you can be employed by someone else and work for yourself.
There are many people who have a full-time or part-time job working for someone else but also have income from work they do outside of that employment.
When you are employed, your tax and national insurance is paid by your employer direct to HMRC after deducting it from your wages. For other income, you will need to register for self assessment with HMRC so that you can declare and pay tax on the money earned from other sources.
To register for self assessment with HMRC, use the following link register for SA
You have 6 months after the end of the tax year in which the income was earned to register. So for example, if you earned casual income in July 2016 you would need to register by September 2017 to declare that income.
When you complete your self assessment tax return form (or ask a bookkeeper to do it for you) the P60 from your employment will be used to give you the figures for the employment section and your other self employed income is declared on separate self employment pages, along with details of any associated expenses.
We are always happy to chat about the registering process, how to declare your income, what is classed as a business expense and many other topics. Contact us for more information.