As I understand it, there are variations depending on whether you are a sole trader or working through a limited company. And all this is assuming that your vehicle qualifies as a commercial vehicle:
Sole trader can claim back a proportion of the VAT, just like you can reduce your income by a proportion of the the cost of the vehicle. The proportion relates directly to the estimated split between business and personal miles, and you should have some evidence - like a mileage log - of how you came to that percentage.
For limited companies, it is a lot more "all or nothing". I run a limited company, and am the only director and only employee. About 15% of my mileage is personal, and this is too much to pass off as "incidental". I have the option of treating a new vehicle as a benefit in kind, and paying a fixed annual amount to the revenue in order to claim back 100% of the expenses, including VAT. Information here:
Van benefits
I also have the option of claiming nothing immediately, and charging the standard 45ppm (up to 10,000 annual business miles) to the company, tax free.
Which option is best for you depends on various factors. As my annual mileage is fairly low and I hope to keep the van for a reasonable amount of time and sell it for a decent percentage of its purchase price, it is actually better for me to go down the mileage route. More pain now but it'll work out best in the end. A big consideration is how well these vans hold their value, as the sale of any company van has to go through the books as profit.