Hi,
As a small business owner myself I understand that budget can restrict us, and it becomes a catch 22, can’t grow without exposure etc etc.
What is your target audience – the students or parents? I also know you want to grow your tutor base. If students are your main target I would suggest looking at Facebook, do some free blog research, maybe a couple of free course on udemy
Example blog: https://adespresso.com/academy/blog/facebook-ads-cost/
I am not a marketing person, but I read a lot and I ask a lot of questions. You are getting GREAT numbers to your site, and you need to understand why they aren’t converting.
I had a friend look at your site for her daughter (year 11) her response was it was confusing to the eye and she didn’t know where to start. Your title on the page “Your Easiest Way to Find a Private Tutor & Music Teacher“ was hard to see on the light background and the search field was not the first thing that jumped out.
She said the first thing that stood out was “Have Questions in Mind” She suggested as a mum looking for a tutor, make the search fields stand out more and just below that have the popular searches line.
DON’T be offended by this, she is a normal mum who I thought would be good to test your site.
I have seen similar sites with a search right in the middle, drive people directly to the part of your site you need.
EXAMPLE: http://wedesignthemes.com/themes/lms/
Like I said I am not a marketing person, simply a business person, and I use any person I can find for feedback.
Good luck 
