I am not in the trade but from what you say you are young and getting little more than the minimum wage, you provide your own tools. I really think you are being exploited.
See if you can work out how much your boss is making from your labour. See if you can find the cost to the customer of a job, and see if u can work out how many days the job takes. You cost your employer £300 a week + on Costs, NI,Pension contributions then ther is insurance, and transport for you. Say that’s £400 a week. Now there are other costs that you need to earn to keep the business going, and your boss pays those. Premises, office staff, advertising etc etc. It would be possible to make informed guesses and work out approximately how much profit he makes from you a year after all the other costs.
He could easily be making £10k a year from you and each of his employees. Does he work at the job himself?
Are you confident to ask for a rise. Don’t ask, can’t get. Have you got any older relatives you could talk to.
You say you don’t really want to leave ... but you can’t, and stay in the same line of work , as you don’t drive. He knows that and will pay you as little as he can.
Driving qualifications will really help you. But that’s been said before.
Good luck, let us know how you get on.