However, the state police rejected the allegations, saying that due process of law was followed at every stage.
Jagtar Singh Johal alias Jaggi was among the five persons arrested earlier this month in connection with the cases of targeted killings, including that of RSS leader Jagdish Gagneja.
Johal, who got married last month, was nabbed from Jalandhar.
The police had claimed that Johal was involved in conspiracy, coordination, funding and arranging of weapons for members of the KLF module linked to the targeted killings.
More From This Section
"If Indian agencies had been keeping an eye on Jaggi for one year, then the British government should also have been consulted in this regard," he said.
"He himself (Johal) claimed that he was brutally tortured," the post read.
AAP MLA from Kharar Kanwar Sandhu had earlier demanded a joint probe with the UK authorities in the case.
On November 19, Punjabi singer and actor Diljit Disanjh had tweeted he was sad to hear about the alleged torture.
Earlier, Punjab police had rejected Canada's National Democratic Party leader Jagmeet Singh's allegations that Johal was tortured.
A police spokesperson said due process of law was followed at every stage, with the accused allowed access to his counsel and family members, as also a team from the UK High Commission.
"Not only did it have sufficient evidence to prove the complicity of Jagtar alias Jaggi in the cases of targeted killings, the police had also ensured that there was no violation of his rights at any stage," he said while rejecting allegations that Johal was framed and tortured.