Samia Shahid, a beauty therapist from Bradford region of northern England,was visiting relatives in Pandori village near Mangla Dam when she was reported dead.
The 28-year-old had been living with second husband Syed Mukhtair Kazam in Dubai, a relationship her family allegedly did not approve of.
"Should this be (an honour killing) case then we must ensure justice is done for Samia and we must ensure this never happens again," Shahid's local MP in Britain, Naz Shah, has written in a letter to Pakistan Prime Minister Nawaz Sharif.
West Yorkshire police said the force was aware of the death and would liaise with the UK Foreign Office and Pakistani authorities.
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A Foreign Office spokesperson confirmed Shahid's death, saying: "We are providing support to the family of a British national who has died in Pakistan, and are in contact with the local authorities to seek further information."
Kazam, a Pakistani national, claims Shahid's family did not approve of their "love marriage" but she moved to live with him in Dubai in May 2015.
"I am sure my wife is killed by the family. She was healthy. And she had no disease. I believe she was killed because her parents were not happy with our marriage," he told the Guardian, which has seen a copy of Shahid and Kazam's British marriage certificate, signed on September 24, 2014.
Kazam claimed Shahid was told that a relative was gravely ill in Pakistan and she flew to Islamabad on July 14.
She was due to return last Thursday but Kazam said he received a call on Wednesday from one of Shahid's cousins saying she had a heart attack and died.
"The family did a postmortem. There's no evidence whatsoever of murder," he said.
Apolice inquiry is under way in Pakistan but no arrests have been made so far.