If you have the time and energy there is no legal reason why you can't do this. In fact quite a lot of people start building up a new business in their free time, and keep on their paid job as a form of security. Then if the business takes off they give up the job. Others like to remain in employment but have a small business on the side for extra income - this is often the case if you're making a business out of something you like doing as a hobby anyway.
If you do decide to go down this route, you have to make sure your paperwork is in order. Generally, your tax and national insurance from your job will be taken care of by your employer, but for your business you need to keep a record of everything you earn, as well as your expenses, and you will probably have to pay your taxes and other contributions separately.
You can find all you need to know here.