It's unlikely to be "controlling prostitution for gain" within the meaning of section 53 SOA 2003, unless the driver is exercising some control over her actual bookings and/or money.
It's "trafficking within the UK for sexual exploitation" - section 59A(1)(a) SOA 2003 (as amended).http://www.legislation.gov.uk/ukpga/2012/9/section/109/prospective
Because of the wording of sub-section (2)(b) it wouldn't be an offence to drive an independent WG to an appointment
because no party is committing a "relevant offence" within the meaning of section 60. Neither is it an offence to drive a girl back from an appointment or home from a brothel.
There's no requirement for coercion.
If convicted, the court can order forfeiture of the car - section 60A.