Though the rat was not found, the pilot returned to Mumbai on Wednesday keeping passenger safety in mind, Air India said in a statement.
Passengers were later flown by a separate aircraft to London.
The aircraft will be fumigated and checked before it is returned to service.
Maintenance workers would have to make sure that the rat did not damage equipment or chew any wires and the plane is certified to be rodent-free, an airline official said.
Air India experienced a number of incidents on Wednesday, according to the Associated Press.
A pilot aborted takeoff from a northern Indian city after a stray dog ran onto the runway as the plane was taxiing.
An official at the airport in Amritsar said the pilot spotted the dog running onto the path of the front wheels of the plane. He applied the emergency brakes and returned the aircraft to its parking bay. All 171 passengers and crew later boarded the same plane which took off for London.
In another incident, an Air India plane from Mumbai was hit by a catering van at the Newark, New Jersey, airport in the United States.
Two weeks ago, a member of Air India ground crew was "sucked into" an aircraft engine and killed.
The technician, who worked for Air India, died when he was working on the plane that was due to fly from Mumbai to Hyderabad.