First tutors is one of the only listings sites that won't cost you anything. Most of the others mentioned here take a large cut of every lesson you teach. FT charge parents a finder's fee but nothing else.
Get yourself on local mums' groups on FB and comment on tuition and education related posts. Giving free advice like this has led to lots of work in my experience.
There is a great FB group for tutors. Search for UK independent private tutors. Lots and lots of great advice on there, like a virtual staffroom.
Before you take on any clients, decide how you're going to operate. Get your prices and terms and conditions set up (look at that FB group for advice) and don't let anyone take advantage of you as a newbie.
If you're going online then get a zoom account and check out bitpaper. If you're doing face to face, decide if you're willing to travel (and how far, if you'll charge mileage etc) or if students will come to you.
Get some public liability and professional indemnity insurance set up. PL is necessary, PI is a personal choice.
I'm a private tutor myself and am happy to answer any questions you might have.