The coach was travelling northbound on the A3 near Hindhead in Surrey at 11.50pm yesterday when it left the road between the Hindhead tunnel and the exit for Thursley. No other vehicles are believed to have been involved.
Three people aboard the 51-seat coach were declared dead at the scene and a fourth passenger was airlifted to Southampton General Hospital with life-changing injuries, Surrey Police said.
Other passengers, some of whom have serious injuries, have been taken to the Royal Surrey County Hospital in Guildford, St Peter's Hospital in Chertsey, St George's Hospital in Tooting, King's College Hospital in London, Frimley Park Hospital and Queen Alexandra Hospital in Portsmouth.
The road was closed in both directions shortly after the incident, and Surrey Police , Surrey Fire and Rescue and South East Coast Ambulance Service all attended the scene, along with collision investigators.
The coach is from the Merseyside area and Surrey Police is working with its counterparts at Merseyside Police, as well as with the coach company, to identify the passengers and notify relatives.
Passengers are being taken to a rest centre which has been set up nearby by Waverley Council.
Surrey Police Assistant Chief Constable Jerry Kirkby said: ''This has been declared a major incident and we are working with our colleagues from the other emergency services and other partner agencies to provide a co-ordinated response in line with agreed protocols.
They also said a casualty bureau number had been set up and people concerned about passengers on board the coach should call. 0800 056 0154.
Surrey Police spokeswoman added: "Officers are carrying out a thorough search of the scene including the coach and thesurrounding area."
