Sole traders and cars

A sole-trader client is looking to purchase a new car but has been refused credit.  She has asked whether the car could be bought in her mother's name and the business use still be treated as an allowable expense.  Her mother has no connection with the business.

My gut instinct is no, but then I wonder if it would make a difference if she went down the approved mileage rather than capital allowance route.  But then I wonder if I'm over-thinking it!

A second opinion would be much appreciated.