He also added that the two sides would instead hold a "virtual meeting in the coming days to launch plans for a transformed India-UK relationship".
Earlier Monday, Downing Street confirmed that British Prime Minister Boris Johnson's trip to India next week has been canceled.
"The decision to add and remove countries from the red list is informed by the latest scientific data and public health advice from a world-leading range of experts", a No 10 spokesperson said.
The situation in India has deteriorated with an extremely rapid rise in cases detected throughout April, which is accelerating.
New Delhi is being put under a week-long lockdown from Monday night as an explosive surge in coronavirus cases pushed the Indian capital's health system to its limit.
This was the first major trip by Mr Johnson post-Brexit and after re-election.
The UK's environment minister, George Eustice said the trip should go ahead despite rising cases in the country. The last scheduled summit in December 2019 was cancelled due to the protests against the Citizenship Amendment Act.
Confirming 103 cases of the India variant had now been detected, Hancock told the House of Commons: "The vast majority have links to global travel and have been picked up by our testing at the border".
India is one of the world's largest markets for air travel and has strong links to the United Kingdom population dating back to the British colonial era.
Imperial College's Danny Altmann said the discovery of the Indian variant should warrant the country being placed on the UK's "red list" - meaning that incoming travellers are subject to a hotel quarantine for 10 days.
The health ministry also reported 1,619 deaths from Covid-19 in the past 24 hours, pushing the toll to more than 178,769.
He told Sophy Ridge: "We've got some of the best genomic studies available in this country, we are very good at genome sequencing for different variants and that work is ongoing".
He added: "After studying the data, and preceeding on a precautionary basis, we have made the hard but vital decision to add India to the red list". The soaring cases and deaths come just months after India thought it had seen the worst of the pandemic.
The British government has said the Indian variant is a "variant under investigation", not a "variant of concern", due to a lack of evidence, so surge testing or forensic contact tracing are not taking place.