However one of the two players admitted to the hospital has died while receiving treatment at the hospital.
The Durham City Rugby club in a message posted on its website said "the Howard and Baty families have requested that their right to privacy is respected".
The 22-member rugby side, Clems Pirates had arrived in Sri Lanka early last week to play a couple of friendly matches.
Mr Baty, also from Durham, who had been critically ill, has also now died.
Catalan secessionists poised to elect new regional leader in second vote
In a series of articles published in online media, for instance, he said it wasn't "natural" to speak Spanish in Catalonia. Spanish is more widely spoken than Catalan in the region, and Spanish speakers are overwhelmingly against secession.
The players, both from Durham, were on tour with one of the club's teams, the Clems Pirates.
Two British rugby players who died after what is suspected to be a drug overdose had visited a night club in Sri Lanka's capital Colombo, shortly before they developed respiratory problems, investigators said Tuesday.
The club previously said that in both cases the breathing problems were non-rugby related.
After emergency treatment a player has passed away early morning on Monday (14) while the other player is now under treatment in the Intensive Care Unit of the private hospital.
Mental Health Awareness week message for Kent - help is on your doorstep
Last year, a Government Green Paper promised a shake-up of children's mental health support with an injection of £300m. This includes ensuring that employers treat stress and mental health problems as seriously as physical safety.
The Foreign Office confirmed it was dealing with the incident: "Our staff are supporting the family of a British man following his death in Sri Lanka, and are in contact with the Sri Lankan hospital services".
"We ask the media to respect the privacy of the families at this very hard time".
However, after returning to the team hotel, two players had developed breathing difficulties and the hotel management had admitted them to a leading private hospital in Colombo.
The British embassy said in a short statement it was assisting the players' families and was in touch with local medical services.
Margot Kidder dead; 'Amityville Horror,' 'Superman' star was 69
Kidder played Lois Lane to Christopher Reeve's Superman in the 1978 film and continued on in that role for the next three sequels. She also made a cameo appearance in the 1987 film about the DC Comics superhero titled " Superman IV: The Quest for Peace ".