Officers are also investigating the possibility that Jackie Issacs deliberately took her own life.
Last night, more than 24 hours after Mrs Issacs was last seen, police had still found no trace of her.
Her 21-month-old son Joey was found naked and semi-conscious at around 7.30pm on Saturday night outside the Thurrock Yacht Club, in Grays, Essex, on the banks of the River Thames. He was taken to Basildon Hospital for treatment for hypothermia where he was last night said to be making good progress.
Mrs Issacs, from Grays, had gone to the club at about 3pm and had a drink at the bar. Staff said she had been in good spirits and bought a ticket for a Valentine's Day dance that evening. The mother-of-three, whose two other children were staying with their father for the weekend, was later seen enjoying the warm weather and paddling in the river with her son.
The alarm was raised several hours later after staff found Joey, along with his pushchair. His mother's clothes, jewellery and watch were found in mud at the water's edge.
Chief Inspector Terry Shearn, of Essex Police, said Mrs Issacs had spoken to staff at the club when she commented on it being lovely weather for swimming, but was advised against it because of the strong current.
He said: "We are growing more concerned by the hour as to Mrs Issacs' whereabouts. We have not ruled out the possibility that she might have drowned while going for a swim in the river. But nobody actually saw her swimming.
"We have also not ruled out the possibility of suicide and also the possibility that for some reason she took off and is in fact safe and well somewhere."
Police, aided by the Thames Navigation Authority, have called in helicopters to search the area. Divers will not be called in until there is a definite area to search.