Their three bodies, all fully clothed, were discovered by a member of the staff in the main 25-metre pool at the Seymour Leisure Centre in Seymour Place, Marylebone, on arriving for work just before 7am.
Police said there were no signs of a break-in or a struggle at the centre, the operation of which has been contracted out by Westminster City Council to a private company, Civic Leisure Ltd of Bayswater. It was not known yesterday how the woman and her children had entered; staff said the centre appeared to be empty at closing time on Friday night. It was believed the woman's car, which contained a baby seat, was found by police outside the centre.
The woman was in her early thirties and the children were a boy aged between five and seven, and a girl of three or four. All three died from drowning, a post mortem at Westminster mortuary revealed. They were believed to come from Notting Hill, west London
"While we are not looking for anyone else in connection with this incident, the deaths are suspicious and the matter will be fully investigated," said a Scotland Yard spokeswoman.
Andrew Yale, spokesman for Westminster City Council said: "At the moment we have no comment to make on this tragic event as police are investigating.
"The council will be holding its own internal inquiry to establish the full facts."
The council received a confidential report from its officers last month asking for money to deal with health and safety problems at its six leisure centres, including the Seymour centre. The report referred to "the absence of adequate regular maintenance" at the Seymour centre.