"We are aware of an incident involving the death of a British national in India. We have offered consular assistance to the family," a spokesperson of the UK's Foreign and Commonwealth Office said.
The FCO had only recently eased restrictions on travel to Jammu and Kashmir in its advice to British nationals.
"The FCO advise against all travel to Jammu and Kashmir with the exception of the cities of Jammu and Srinagar, travel between these two cities on the Jammu-Srinagar highway, and the region of Ladakh," reads its latest travel advisory for the region, updated on April 2.
"There has been an overall decline in violence in the state in recent years and an increase in the numbers of Indian and western tourists. There have been no recent reported attacks on visitors in the cities of Srinagar or Jammu," it adds.
A Dutch man, 43-year-old Richard De Wit, has been detained by police after 24-year-old Sara Elizabeth was found dead inside her room in a houseboat on Dal Lake.
The woman had apparently been stabbed and local police said she was found in a pool of blood with a sharp knife nearby. Senior police officer Abdul Ghani Mir has been quoted here as saying that the man was picked up as he tried to flee the valley with only his passport.
"The Dutch national had fled from the houseboat in the night, leaving behind his belongings. He was trying to flee from the valley, carrying only his passport. We flashed an alert for his arrest," he said.
The body has been sent for medical examination to determine whether the woman was sexually assaulted before being killed.
The British tourist had been staying on the houseboat for over a month and the Dutch man had moved into an adjacent room two days ago. Local police are investigating whether they knew each other.