In very simple terms, during the current tax year, which will end on 5 April 2019, everyone can have an income of up to £11,500 without paying any tax (but see the notes below). Don’t forget that income is the total of what you have been paid by clients less your business expenses.
The fact that you’re not liable to tax doesn’t mean that you don’t have to tell HMRC you’re self employed until you become liable to pay tax.
Once you start to be self employed (in other words start to be in business) you have to tell HMRC that you are self employed. The time limits to register are quite reasonable. Registering sooner rather than later is probably best to make sure you don’t leave it too late (with possible penalties for late registration) and to avoid HMRC starting a tax inquiry because they have discovered you’re self employed but aren’t on their system.
Notes:
Even though you will not pay any tax until your income exceeds £11,500 you may have to pay national insurance
If your income exceeds £6,205 you will have to pay Class 2 national insurance of £2.95 per week
And, in addition to Class 2, if your income exceeds £8,424 you will have to start paying Class 4 national insurance on the excess at 9%.