Britain effectively imposed a diplomatic freeze on Mr Modi for 10 years over anti-Muslim violence in his home state of Gujarat in 2002, but reinstated relations with him in 2012 as part of a general bid to boost ties with India.
“Congratulations @narendramodi on victory in India’s elections. Keen to work together to get the most from UK-India relationship,” the official Twitter account for Mr Cameron’s 10 Downing Street office quoted the prime minister as saying.
British Foreign Secretary William Hague also sent congratulations to Mr Modi and said he would “look forward to forging an even closer partnership with India in the months ahead.”
“The UK has strong ties with India and the British Government looks forward to working with the new Indian Government to build on this relationship and deliver security, growth and prosperity for both our nations,” Mr Hague said in a statement.
Mr Modi’s hardline Bharatiya Janata Party (BJP) looked set for a first single party parliamentary majority in India for 30 years, after apparently wiping out current premier Manmohan Singh’s Congress party in the polls.
Mr Modi was boycotted by the US and European powers over the 2002 Gujarat riots that left around 1,000 dead.
But Britain, which is the former colonial power in India and has a large Indian-origin ethnic population, sent its ambassador to India to meet Mr Modi in October 2012, saying that “active engagement with Gujarat” was the way to boost relations.