You'll need to get your business head on as well as your teaching head.
I've been full-time tutoring for many years now, in addition to Alevel question setting, exam marking and various other bits for the exam board.
A few tips:
You'll need a fairly rigorous set of terms and conditions, otherwise expect to be messed around. Most people are wonderful and reliable, but the few that are not can eat up a considerable part of your time.
Register with HMRC as self employed as soon as you start advertising, not when you get your first student and think about whether you'll do your tax returns yourself, or whether you will want/need an accountant. Personally I use an accountant because the amount of time she saves me vs doing it all myself makes her fee worth it.
Be prepared that you'll have to chase some parents regularly for prompt payment. This will use up a lot of time unless you set expectations early and stick to it.
Think about how you want to deliver tuition.
Travel to students is time-consuming and expensive, but you do see students in their own homes and that keeps work separate from home life. You can end up with a logistical nightmare though trying to coordinate travelling from one home to the next, students availability and what you do between sessions if you have cancellations or get stuck in traffic.
Delivering tuition at your home is more convenient, but do you have a quiet area which won't impact on the rest of your family massively? If you are tutoring face to face either in their home or yours, think about safe-guarding. No tutoring in bedrooms and for minors there must always be another adult in the house. Think about seating and ensuring the student always has unhindered means to exit the house (including leaving the door unlocked) and also what will you do if a parent fails to collect their child on time and you have another session booked in following. Do you have somewhere for the student to wait for their parent whilst you start on the next session.
Online is easier in many ways, but requires more imaginative approaches to keep things interactive. It also takes longer to build close relationships with your students, which ultimately helps their progress.
It is a fantastic job (I've been doing it for 13 years full-time and absolutely love it), but not always as easy to make the transition as people think because it's a very different job to teaching in a school. Yes you don't deal with SLT, but you do have a lot of other things to think about if you want to make a serious living.