Up to one in five toddlers can open medicine bottles and chemical containers, even if they have child-resistant tops, safety experts warn.
Pills can look like sweets to children
The Child Accident Prevention Trust stressed parents should store potentially dangerous products safely.
Every year 25,000 under-fives are taken to casualty, suspected of swallowing substances ranging from medicines to household cleaning products.
One in five are admitted to hospital for treatment.
At the start of Child Safety Week, the trust is warning that bottles and packs of colourful pills are a "devil's sweetshop" for toddlers.
It warned: "Child-resistant tops are now commonplace on most medicine bottles and household chemicals - but they are child-resistant, not child-proof."
And it says many pills now come in pop-out packs which are even harder to make child-resistant.
The trust says common painkillers are the most frequent cause of childhood poisoning, responsible for one in four hospital admissions.
They are often taken from handbags and bedside tables.
Many bathroom poisonings happen after toddlers have drunk bleach or toilet cleaner left by the side of the toilet.
The trust says just six strong aspirins could harm a toddler, and one or two mouthfuls of toilet cleaner could cause internal burning.
Dr Ian Maconochie, a consultant paediatrician at St Mary's Hospital in London, told BBC News Online: "If a child drank a lot of really strong bleach or battery acid, they could harm the gullet and require lots of operations in the future."
He said a "significant number" of the 18,500 children who attend his unit each year are there because of things which could have been prevented.
"The most vulnerable groups are children under five, because they are very inquisitive.
"They tend to be nosy. They get hold of things like tablets and easily take things that they shouldn't."
He added everyone who has small children coming to visit should take care. "Children with grandparents often go to their houses and take their grandparents' medication - they find them in their handbag or kitchen drawer."
Katrina Phillips of the Child Protection Trust said: "Parents should not be lulled into a false sense of security - child-resistant tops are not child-proof.
"They need to keep all medicines and household chemicals locked away or well out of sight and reach."
She added: "Don't tempt fate and leave your child's safety to chance. Just a few simple checks could save you and your child a harrowing hospital visit - or even save their life."
A spokesman for the Royal Society for the Prevention of Accidents (RoSPA) said: "We have seen a reduction in the number of poisonings within the home which involve children.
"But parents still need to store dangerous products out of children's reach - and that can include things like perfume and aftershave."
The trust advises families to:
- Store all medicines high up, well out of reach and sight of young children, preferably in a locked medicine cupboard
Store all household cleaning products such as bleach out of sight, high up out of reach and in cupboards with child-resistant catches
- Never leave tablets in a handbag or on a bedside table - these are favourite places for toddlers to find them