Two paddle boarders who were rescued after being swept more than 10km across Victoria’s Port Phillip Bay on Christmas Day say they are exhausted and shaken but grateful to have survived.

Victoria police said the pair set out from Portarlington on the Bellarine peninsula about 3pm on Thursday but drifted out into the bay when conditions deteriorated and were swept all the way to Wyndham harbour in Melbourne’s outer west.

They were among six people rescued in three separate potential drowning incidents in Victoria on the same day, police said.

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The two paddle boarders were a 51-year-old woman and her 17-year-old stepson, the ABC reported.

After their family raised the alarm just after 5pm, ground police officers, air wing police helicopter officers, Life Saving Victoria and Queenscliff coast guards went looking for them.

Police said at about 6.20pm air wing officers spotted the pair, who were not wearing lifejackets, lying on their paddle boards and waving for assistance. Apart from being exhausted and cold they were not physically injured, police said.

In a statement released through police, the pair said they wanted to express their sincere thanks to everyone who was involved in their rescue.

“We are so grateful for the outcome but still trying to come to terms with how quickly a beautiful, carefree afternoon turned into an almost tragedy,” they said.

“We are exhausted, very shaken and feel so lucky we were able to stay together. We commend the efforts of all the agencies involved.

“The decisive and quick action led not only to our rescue, but our survival. Thank you so much.”

In another Christmas Day incident, police said they were called to Lake King in Paynesville following reports a kayaker was in trouble about 1.30pm.

Police said officers were told the man was seen struggling before his kayak rolled and had not been seen for about two hours.

Water police, air wing and the coast guard searched for the Hoppers Crossing man, who was spotted by the police helicopter just before 3pm, picked up by the coast guard and returned unharmed to shore, police said.

Police said they were also called out to Westernport Bay after a mother and her two teenage daughters got into difficulty while kayaking near the Corinella jetty about 2.10pm.

The trio had attempted to retrieve an adrift kayak when the current and strong winds swept them a significant distance from shore, police said. They were all wearing lifejackets.

The woman and girls had ended up about 1km from the shore line and police said local officers coordinated with the Westpac rescue helicopter to winch them to safety.

They were dropped back to Corinella without injury, police said.