You are in a Catch22 on two situations - the ownership of the business and the VAT.
Regarding the business, you either set up a limited company and channel all the expenses/profist through that business, taking whatever you choose in income for yourself, as and when the business can afford it. You pay corporation tax at 21% on the profits of the business, and any income you take out reduces that profit (so reduces the corporation tax) but then you pay PAYE tax and NI on it, as you are an employee of your own business of which you are also a director.
Or you don't do the above and keep records of expenses/income, and declare it to HMRC as self-employed earnings. With the method, each tax year you would have to make a declaration of the income/expenses and pay personal on any profit. Look here for how self-employment and self-employed tax works.
http://www.hmrc.gov.uk/selfemployed/
With the VAT, you can register the business (for either a limited company or self-employed) whenever you like, you only have to do what tamborine suggests if your turnover goes over the threshold he quotes. It really depends where you are sourcing the cars from. If you are buying through the trade, they would have (generally) to be charging VAT on the transaction, which you could offset. You could also offset the VAT on other expenses like petrol that you quote. But the downside is that you could have no choice but to charge VAT to your customers.
If you are buying most of your cars from private sources where no VAT is charged to you, it would be pointless registering for VAT on the business as you would have no choice but to charge VAT to your customer still.