Your client can either claim the authorised mileage rate (40p,45p or 25p) for the business miles they do. Or they can claim a portion of their motor expenses. The portion claimed depends on the split between personal and business miles. If they use the car 25% for business then they claim 25% of their expenses.
The milage that Kris states also factors in the cost of the service, MOT, and wear and tear on the vehicle. so none of them can be claimed either (unless you dont have milage then use the 'formula' that Kris has said about splitting the expenses)
I've had a client like this this year, didn't keep track of milage, only the amount of fuel she put into it and the bills for maintence. In the end i added it all up and halved it as it was her own personal car. I've found in 6 months ive made more money (myself) by claiming milage than I would have if I had just kept reciepts! :/ (maybe a point worth telling you clients, providing they dont do excessive amounts of milage)
If the vehicle is a fixed asset in the accounts then the road tax can be claimed, if its not in the accounts then other motor expenses shouldn't be included as there is no business vehicle that they relate too, except parking as this is a specific expense for the business journey.
If this is the case then when you do use a private vehicle for business purposes then mileage can be claimed as stated above.
You asked 'what if it related to a van used by a client'. Again if it was a business van and in the accounts the same would apply as my first sentence.
If the vehicle in the accounts is used privately then a proportion of motor expenses should be added back on the tax computation & also the same proportion deducted from the capital allowances claimed.