The family of the mother and two children killed after being swept away by heavy seas on Sunday spoke today of the "heartbreaking tragedy".

They paid tribute to Kim Barrett, 33 and Aimee and Luke Greenwood, from Spen Bank, Leeds. Aimee's body has not yet been found.

Ms Barrett died with Aimee, 13, and Luke, 11, at Scarborough's North Bay during a day out. Aimee and Luke were playing on a slipway on Royal Albert Drive when they were hit by a wave and dragged into the sea. Ms Barrett jumped in to try and save them.

Last night Coastguard officials were forced to give another safety warning after 15 children were seen wave dodging on the same slipway on Monday evening, just hours after the grieving families had visited the scene.

Yesterday Ms Barrett's parents, brother, sister-in-law and cousins issued a statement through North Yorkshire Police.

It said: "Kim was a very thoughtful and caring mother, daughter and sister. She thought the world of her children and would always put her family's needs before her own. Kim was generous, outgoing and touched all she knew.

"Luke and Aimee were fun-loving children with a bright future and so much to look forward to. They were bubbly and happy children and they always had a smile for everyone.

"In one heart-breaking tragedy we have lost them all. It is devastating to consider a future without those we love so much."

They also thanked the emergency services, and a surfer who dived into the water to help.

Ms Barrett's boyfriend Jason Johnson, 34, of Horsforth, Leeds, and his eight-year-old son Alec survived the incident.

Yesterday coastguards patrolled the beaches around Scarborough in a bid to find Aimee's body, but found no sign of the teenager.

Questions have been asked about what can be done to prevent it from happening again, but Scarborough Borough Council said clear warning signs are in place.

A spokeswoman added that if any issues are raised by the coroner's investigation they would be looked into.

It also emerged yesterday that another family had a lucky escape on Sunday when a father took his children to the water's edge on a slipway in Whitley Bay.

A BBC cameraman saw a man and three boys deluged by a wave. The father was forced to cling onto his youngest son, aged three or four, holding him by the arm and hoisting him above the water.