"The big expectation from India will be for it to fulfill the democratic mandate of peace and prosperity,"Labour party chair Harriet Harman said.
John Spellar, the Labour MP for Warley in the West Midlands said, "India has chosen who their leader is and in the event that the exit polls are correct, then the world will work with Mr Modi, and work with him for the benefit of both stability in that part of the world but also in terms of raising the standard of living of the people of India."
An official freezing of diplomatic ties with Modi had been initiated under the Labour-led government in the aftermath of the 2002 Gujarat riots.
However, the party leadership has recently been making several overtures to reinstate ties with Modi, who if exit polls prove to be correct could take over as the new Prime Minister.
Labour Friends of India chairman and MP Barry Gardiner had tried to set the ball rolling with a letter inviting Modi to the House of Commons to speak on "The Future of Modern India" last August.
"The invitation is a culmination of several years of engagement between senior representatives of the Labour Party and Narendra Modi," the Labour MP for Brent North had said back then.
Modi had politely declined the offer.
"Clearly Mr Modi comes with a reputation, and the fact that he was on the banned list in the UK and the US for several years is going to present challenges for all the parties, Labour included," said Yasmin Qureshi, Labour MP for Bolton South East.