The harbour authority said in a post on social media that the spill started at about 21:30 BST on Monday.
“We will put up signs at the swim zone and the bathing beaches, which will remain in place until we are advised the incident is over,” said the authority.
SWW warned on its website, external of an “unplanned interruption”.
“Our teams are working hard to fix a burst rising main at our Mayor’s Avenue pumping station in Dartmouth,” it said.
“We are using tankers to take as much of the flow from the pumping station to the nearby waste water treatment works as possible while we work to complete the repair as quickly as we can.”
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