The official guidance states: "There is no automatic exemption from MoT testing for vehicles used under a trade licence. A vehicle used under a trade licence is only exempt from the MoT testing requirement when driven during or on completion of repairs, or when driven to and from a pre-booked MoT test."

You shouldn't test drive a car with no MoT because it's on trade plates, the only reasons this vehicle can be driven are to/from an MoT or to test the condition of the car when it's undergoing repair work. If caught by the police, you could get into trouble for driving it when you know it doesn't have an MoT.