The call comes from the Royal Society for the Prevention of Cruelty to Animals (RSPCA). It says the 1976 Dangerous Wild Animals Act is weakly drafted and enforced.
Its chief veterinary officer, Chris Laurence, said: "Exotic animals do not make suitable pets because of their specialist needs - but welfare problems can be even further compounded when that animal is dangerous and the owner is inexperienced or left without expert guidance or monitoring.
"We feel strongly that snakes such as large pythons - which are capable of killing or harming a child or toddler and are now commonly kept as pets - should be added to the list of species covered by the act."
Beady eye
One case involved a couple who had a pet boa constrictor, bought when it was only 18 inches (45 centimetres) long. It grew in five years to eight feet (2.4 metres), but was still allowed to roam the house freely.
When the couple brought their new baby home from hospital, the snake tried repeatedly to approach it, and became aggressive when thwarted.
Diana Lewis of the RSPCA said: "Every time the couple allowed the snake anywhere near the baby, the creature would head straight towards it.
"A constrictor snake could kill a baby with no problem at all. They were right to call in the RSPCA."
Nasty bedfellows
In Derbyshire RSPCA officials removed a five-foot (1.5-m) alligator from a flat, where it had been living in a pond liner in a small bedroom.
In another case, a man bought what he believed was an exotic lizard in an Essex pub for £20 ($28). It measured 12 inches (30 cm).
It proved to be a spectacled caiman, a type of crocodile which can grow to seven feet (2.1 m).
A man with a collection of deadly snakes in his flat in Sheffield told the RSPCA he knew he needed a licence for the animals under the act, but had chosen not to apply for one.
The eight snakes included gaboon vipers, puff adders, sidewinders and a copperhead. The RSPCA said they were aggressive, and one bite could have proved fatal.
Protection needed
Elsewhere in Yorkshire, the society and the local police retrieved two Eurasian lynx being kept in a shed with only a wooden clothes peg to prevent them escaping.
The RSPCA wants the UK Government to:
Chris Laurence said: "We cannot wait for a tragedy to happen before controls are introduced."