But Nick Starling, of the Association of British Insurers, said: "While we understand the desire to reduce the number of attacks by dogs, making insurance compulsory for all dog owners is much more difficult than it looks.
"There is currently no stand-alone third-party insurance cover for the owners of dangerous dogs, and no desire by insurers to provide cover against this very high risk.
"Making it compulsory for pet owners would still not make it compulsory for insurers to offer the cover.
"While pet insurance policies will usually include third-party liability cover for dog owners, this would not cover dangerous dogs as defined under The Dangerous Dogs Act, and other specified breeds."
He added: "Even if third-party insurance was available, how would such a system be enforced, especially as many of the owners of dangerous dogs would be unlikely to take out insurance, even if it was compulsory.
"And would someone who was attacked by an uninsured dog be entitled to compensation, and if so from whom?"
Postman Paul Coleman describes how two dogs attacked him on his delivery round
The Conservatives said the government had allowed the problem to get worse, with the number of people convicted for allowing their dogs to cause injury more than doubling in the past decade.
Liberal Democrat home affairs spokesman Chris Huhne said penalties for dangerous dog offences had to be "sensible" and that any changes to the law had to be "simple and strong".
The proposed insurance plan would not apply in Scotland. However, a backbench bill proposed by the SNP's Christine Grahame is currently being examined by the Scottish Parliament.
The Control of Dogs Bill would allow councils to impose restrictions on owners who failed to control their pets.
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