The Parliamentary Group for Animal Welfare plans to put its concerns to the Department for Environment, Food and Rural Affairs (DEFRA) in the new year.
"People are stealing dogs with a criminal element coming into it," said group chairman Neil Parish.
Parish believes more action is needed to reduce the number of pets being taken.
"I think government is becoming aware of it but probably needs to become much more aware of it. The government have got to make sure that the public are also much more aware of it," he was quoted as saying by the BBC.
Of those, 457 were identified as being stolen during that period, the report said.
The research found that 49 per cent had been taken from gardens, with 13 per cent taken from people's homes.
However, the Dog Lost organisation said the numbers being snatched could be even higher.
"Quite often a dog is perhaps perceived as just being missing and it's only after it's been missing for a while that an owner actually finds out it's been stolen," said Dog Lost's Nik Oakley.
One woman from West Yorkshire said she had her pet stolen by a man who broke into her home earlier this month.
The man threatened her with a knife before stealing her two-year-old French bulldog.
The figures collated by Loughborough University found that rewards were offered for around 42 per cent of the dogs taken.
But Dog Lost warns that specifying certain amounts for rewards could lead thieves to take advantage of owners searching for their missing pets.
"If you put a price on it, then that reward is always negotiable upwards because thieves know that people are desperate to get their dogs back," said Oakley.
A DEFRA spokesperson said: "Lost and stolen dogs cost taxpayers and welfare charities 57 million pounds every year.
"We are combating this problem by bringing in compulsory micro-chipping by 2016. This will make lost or stolen dogs easier to trace and gives owners peace of mind," the spokesperson said.
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