The firm advised using measures like having scrapers, de-icers and checking tyre pressure before setting out.
It also said that once on the road, drivers should allow plenty of time for the journey, keep a good distance between them and the driver in front and take care when manoeuvring, with sharp turns to be avoided if possible.
An additional tip was to stop for 15 minutes every two hours if undertaking a longñdistance trip.
Head of Insurance at M&S David Wells said: “Motorists living in areas where roads are icy should heed police advice and not make unnecessary journeys.”
Earlier this week, Swiftcover.com said the first week after the new year bank holiday weekend saw 75 per cent more claims than usual as the icy weather took its toll.