Jagtar Singh Johal, a British national was arrested on November 4 while he was on a visit to his hometown in Punjab (India) for his wedding.
The police have accused him of being complicit in the targeted killings in Punjab. It has been alleged that Mr Johal funded the purchase of weapons to kill Hindu leaders.
Mr Johal’s family has accused the police of keeping him in custody without any charges and torture.
Members of the Sikh community have staged demonstrations against Mr Johal’s arrest, who they claim is an activist working to spread awareness about the 1984 anti-Sikh violence in New Delhi in which thousands of innocent Sikhs were massacred following the assassination of the then Indian prime minister, Indira Gandhi.
The British Foreign Office said Mr Johal’s case was being taken very seriously.
"We take any allegation of torture very seriously, as indeed would the Indian government. It is completely unconstitutional - it is offensive to the British government - and we will work very closely to investigate and of course will take extreme action if a British citizen is being tortured," Minister of State at the Department of International Development, Rory Stewart said in the House of Commons.
On Monday, British Prime Minister Theresa May said the government was "concerned" about Mr Johal's case, the BBC reported.
"Representatives from the Foreign Office have met with Jagtar Singh Johal and obviously are pursuing the case and watching what is happening with concern and will take action (deemed) necessary,” British Prime Minister told the BBC on Monday.
The chief minister of Punjab, Captain Amarinder Singh said the police was following the due process and denied that Mr Johal was tortured.
Mr Johal has been accused of being involved in the conspiracy, coordination, funding and arranging of weapons for members of a banned militant outfit that was busted for the “targeted killings” in Punjab.
