They had been touring the country with Durham-based Clems Pirates RFC.
The Clem's Pirates said they will continue their charity work in Galle, a city in Sri Lanka's southwest, as a mark of respect to Mr Howard and Mr Baty.
Another British Rugby player who was admitted along with Bett Thomas Reid passed away that very night with the same symptoms.
Mr Baty's teammate, Thomas Howard, 26, died on Sunday - also as a result of breathing difficulties.
The pair were admitted to hospital after struggling to breath during a tour of Sri Lanka.
Howard, 25, died in hospital Sunday, according to a statement from Durham City Rugby and Football Club (DCRFC) and the UK Foreign Office.
The Police said the British rugby player had arrived in Sri Lanka to play a friendly game.
Several people were evacuated from their homes due to the heavy downpour on Sunday but as the rains ceased by Monday morning, the situation was normalising, Disaster Management Centre's spokesperson Pradeep Kodippilli was quoted as saying by Xinhua news agency.
Police have told the families present in Sri Lanka the judicial medical officer gave an open verdict and sent body samples for further analysis.
'We ask the media to respect the privacy of the families at this very hard time.
After the match, the team went out for a meal before they visited a nightclub in the Kollupitiya area of the city.
Durham City Rugby Football Club, which oversees the team, confirmed Mr Howard died after "suffering breathing problems".
Clems Pirates are described as a "fine example of veterans rugby", known in the northeast of England for "their sheer enthusiasm, terrific tours and their fundraising efforts".