Hi, it's interesting to hear this from your perspective. When you go online and Google a "tutor" or "maths tutor", all the big agencies and companies with bigger advertising budgets and larger websites with better SEO really do come up first (paid or organic) and finding independent tutors means diving several pages further.
Also, while I've been tutoring for 20 years, I've rebranded as I was evolving as a tutor, so I've changed domains a few times, and each time that also meant starting from scratch, losing the advantage of big brands, hence googling independent tutors won't always get you the results easily.
So, if you're looking for an independent tutor (there's plenty!), you may need to change the way you're looking for them.
For example, if you're on Facebook, you can find a lot of groups where tutors advertise (local groups, UK-wide groups, specialised groups for anything from home education to GCSE... literally every possible angle of tuition one might be looking for).
Word of mouth is also a way, for sure. Both from parents and tutors, too. I got plenty of recommendations from colleague tutors (and I recommend them, too) - as we often know what we specialise in, so we can actually refer well to each other.
This is actually how most of my students find out about me. The odd one here and there finds my website and contacts me directly.
So that's the reality of being an independent tutor. I hope your search went well. I noticed this is an older post, but I hope my reply will be useful for some who are still unsure how to find independent tutors 😊