This paints a rather different picture. It now appears that this isn't actually a company car at all. A company car is one which the company owns and makes available to the employee for private use, i.e. the employee is *given* the benefit of car use (and the notional taxable value of that benefit is calculated by some obscure formula).
But in this case you are saying she has to "buy" the "benefits" herself, but is given a salary top-up towards their costs. In this case I believe it would only be the extra £2800 which would be taxed, in effect her salary for tax purposes would be £30800, and there would be no extra "car benefit" charge, since it's not a company car. It is in fact her own car (which she leases from a car company).
If the car is also to be used for work (bearing in mind that commuting is not "for work"), she should claim 40p/25p mileage allowance for any work-related travel. Even if she will not be paid by her employer for this, it is still deductible from her taxable income.