You won't have to pay "regular" taxes just like your parents do on their income.
In fact, the only taxes you have to pay will be regarding your health insurance.
Paiement of National Insurance depends on the amount you expect to earn.
In other words, if your profits do not exceed £5,965, you will not have to spend a dime on taxes ! Between £6,000 and £8,059 you will need to pay £3 a week. From £8,060 up to £11k you will need to pay both Class 2 and Class 4 (9% of your annual profits).
Bonus: Class 2 National Insurance will disappear in 2018 ! Hence, if your profits are inferior to £8,060 you won't have to pay anything 😉