Your situation is largely analogous to that of a self-employed private hire driver, who is supplied with work by an office that handles calls from potential customers and which then radios him to offer him the work (but with the rate being charged to the customer determined by that company, rather than by the driver).
HMRC generally accepts that such drivers are genuinely self-employed unless the company forces them to work at specific times or otherwise acts as an 'employer' (e.g. by prohibiting drivers from doing work other than that offered through the drivers' radios).
It can be a bit of a grey area, as the arguments over the employment status of Uber drivers in London have shown but, if you're free to accept or reject new students and not barred from accepting students who approach you directly, then it would seem likely that HMRC would see you as being self-employed.