The “Junior Swim Card” promotional offer costs £22 and gives children six weeks of unlimited swimming sessions at leisure centres run by East Riding of Yorkshire Council.
But the authority has faced criticism because it does not apply to East Riding Leisure Bridlington or South Cave’s leisure centre.
One angry mum, who wished not to be named, said: “They obviously don’t care that Bridlington kids, many of whom live on or below the poverty line, will miss out yet again.
“They have built a facility aimed at visitors and not for locals. When Scarborough get their water park up and running, they’ll be desperate for customers!”
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And dozens of fed-up mums and dads on the Bridlington Free Press’ Facebook page also voiced their disappointment.
Joanne Mason said: “My daughter used her swimming pass loads last year in the holidays at the Sports Centre.
“If they were going to do this, then why didn’t they keep the Sports Centre pool open for the locals to use?”
In a response to one parent’s complaint, a staff member at East Riding Leisure Bridlington e-mailed: “The ‘Junior Swim Card’ promotional offer is primarily intended to attract people to use the indoor swimming pools during what can be a fairly quiet time for indoor swimming in normal swimming pools because if the weather is good, people tend to want to do things outdoors.
“East Riding Leisure Bridlington is clearly in a different position because it is a centre aimed at both residents and visitors and has greater usage during the Summer.
“The pricing for these facilities is already very competitive on what is already a very good offer.”