If you buy or lease a car privately and charge your company for 15,000 business miles annually, you will get £5,750 per annum in tax free payments (10,000 @ 45p per mile + 5,000 @ 25p per mile). The company will save 20% of that in corporation tax if it makes profits up to £300,000 per annum, slightly more its profits are higher than that, at least until there is only one corporation tax rate.
If the company buys the car, it will be able to claim capital allowances at 8% per annum on a reducing balance starting at £58,000 (see here). It will not be able to reclaim the VAT unless there is no private use of the car. If it leases the car, it will be able to claim a deduction for the lease payments and reclaim 50% of the VAT (see here).
On a £58,000 (list price when new) car with 280g/km CO2 emissions, for 2014/15 (1 November 2014 say to 5 April 2015), the car benefit will £8,676 and the car fuel benefit will be £3,246. You will pay tax on £11,922 at 40% (£4,769) and the company will have a Class 1A NIC liability on £11,922 at 13.8% (£1,645).
On a £58,000 (list price when new) car with 280g/km CO2 emissions, for 2015/16 (6 April 2015 to 5 April 2016), the car benefit will £21,460 and the car fuel benefit will be £8,029. You will pay tax on £29,489 at 40% (£11,796) and the company will have a Class 1A NIC liability on £29,489 at 13.8% (£4,069).
There is a car benefit and fuel benefit calculator here and the appropriate percentages can be found here.
I hope this helps but let me know if you have any further questions.