The man, known only as David T, and his 10-year-old son were stopped from going into the pool at Clissold Leisure Centre in Stoke Newington, east London.
Last night embarrassed management at the complex said staff were wrong to turn customers away from the designated 'men-only modesty session' on Sunday morning.
The council says the special early-morning get-togethers are aimed at community groups who have strict rules on segregation.
A man and his 10-year-old son were stopped from going into the pool at Clissold Leisure Centre
But the dad and his lad were prevented from swimming when they turned up at 9am on Sunday.
David T said: "I arrived at the pool to discover that they were holding what staff described to me as 'Muslim men-only swimming'.
"I asked whether my son and I could go as we were both male. I was told that the session was for Muslims only and that we could not be admitted.
"I asked to speak to the duty manager, who confirmed that this was the case."
He added: "I asked what would happen if I turned up and insisted I was Muslim.
"The manager suggested that they might ask the Muslims swimming if they minded my son and I swimming with them.
"If they didn't object, we might be allowed in."
The men-only modesty swimming sessions take place every Sunday from 8am to 9.30am.
Two websites have been advertising the sessions for Muslim men only.
But a leisure centre spokesman said staff were out of order to refuse people entry for being non-Muslim.
He said: "The member of staff the user spoke with at the time was mistaken when referring to the session as Muslim only.
"The men's modesty session is not a private hire and is, therefore, open to the public. Muslim men and others can attend.
"Staff cannot ask your religion on entrance and you won't be refused entry if you don't appear to be Muslim."
A spokesman for Hackney Council said: "None of Hackney's leisure centres have religiously segregated swimming sessions in their public timetables.
"In common with most public swimming facilities, there are single sex sessions, and this session was men only.
"The member of staff in this situation made a mistake... Hackney Council would wish to apologise to any member of the public who was given incorrect information."