I wouldn't say there's a "place" to find students - You mainly do it from advertising. Some websites exist for online tutoring, and I would certainly recommend you look online there, but I don't personally use them; I just generally prefer in-person tutoring. Still, they seem like a great and vital resource for advertisement.
I think a big way to advertise for in-person tutoring is through local groups on social media; My city has many facebook groups like "Manchester Community Group" or "Brighton Spotted", for examples, and I'd recommend you post on there about your tutoring. I think this is a great way to advertise as you have to keep in mind, you're not necessarily advertising to the student, but to the parent's of the student. The student won't find the tutor, the parent's will, and so you want them to remember you through those social media apps. Word-of-mouth is a big thing with things like tutoring and clubs.
You could also post up physical signs? I haven't tried this, but I imagine it works quite well to advertise. Also, be sure to reach out to family members about your tutoring; Someone's friend of a friend of a friend is always taking their GCSEs, and you can often find students that way.