Like any business you need divergence from competition, if there isnt any then it comes down to price.
Just a thought but your USP could be the vehicle you use to give the lessons - something different than the rest of the crowd, this may make competition less relevent and still allow you to command a half decent hourly rate. If this is the case you would need to maybe even change/funnel your target market - but would that limit you? Would there be enough fodder out there to keep you going?
An example would be teaching school leavers/sixth formers in a performance vehicle(of course within limits), it would engage every young lad in your area, they would book with you, not your competitors as you are offering divergence and have a USP. Would it eliminate competition? No Would it give you an edge? Yes! You then need to look into the demographics of your geographic area and see if the age group would be able to sustain your business
I think in this game if you are not different then the only thing that will attract customer is price, reputation is built with time and many would have already bet you to it on this one.