They said: “Our thoughts are with her family and friends at this difficult time.”
The two children were rescued off the coast of Bimini, police in the Bahamas said.
In a statement posted on social media, the Royal Bahamas Police Force said officers received reports shortly after 10:00 local time on Tuesday that a woman had been found unresponsive at the North Bimini Ferry Dock.
It added after she was swept away, she was brought to the ferry dock where CPR was given.
Leanne was then taken to a local medical clinic but was confirmed dead there, the police force said.
It said an autopsy would be conducted but “foul play is not suspected”.
A spokesperson for the Foreign Office added: “Our thoughts are with the family of a British woman who has died in the Bahamas.
“We are in contact with the local authorities and providing support to her family.”