More than 5,000 dogs have been reported stolen to police forces in England and Wales since the start of 2013, a BBC investigation has found.
Figures obtained under the Freedom of Information Act show a 22.3% rise in reports in two years.
Gareth Johnson, a Conservative MP in Kent, has called for a specific crime of pet theft to be introduced.
The Ministry of Justice (MoJ) said courts were told to account for emotional distress.
Figures from police forces who replied to the BBC's request show at least 5,288 dogs reported stolen since 2013.
They indicate 1,490 taken in 2013, 1,599 in 2014 and 1,776 in 2015. In the first four months of this year, there were a reported 423 thefts.
Some forces reported the theft of several dogs at the same time as a single offence.
Thieves target Staffordshire bull terriers and tiny toy-designer breeds, like miniature French bulldogs, and pugs, popular with celebrities, the figures suggest.
Nik Oakley, from Dog Lost - which reunites lost and stolen dogs with their owners - said gun dogs such as Labradors, cocker spaniels, and springer spaniels were being taken for working purposes and illicit breeding.
Anna Rigano, from Forest Row in East Sussex, had her Jack Russell, Buster, stolen in March.
"I went to the field with some friends... I let him loose because I felt confident and he knew the area, and he never really goes away from me for very long.
"I started calling him and he didn't come to me, I think he was picked up because he was such a friendly dog and I've never found a body," she said.
Vet Louise Marsh, from Woking in Surrey, was reunited with her pet dog Toby after he was stolen from her street in 2014, and later dumped in a field in Kent.
The Border Terrier was discovered following a high profile social media appeal supported by the tennis player, Andy Murray, and the band, One Direction.
Ms Marsh said some were stolen because they were worth a lot of money for breeding.
"A British bulldog, for example, you can get £1,800 for a puppy.
"So if you can get hold of a British bulldog bitch, and get her pregnant, you're looking at thousands of pounds worth of puppies," she said.
It is a legal requirement for all dogs to be micro-chipped but vets do not have to routinely scan new dogs brought into their surgeries.
"Many dogs may stay lost or stolen until they actually get scanned by somebody," said Ms Oakley.
"We want it to be compulsory to all vets, local authorities, rescuers, to scan every dog that goes past them," she said.
Gareth Johnson, the MP for Dartford, wants the government to recognise the growing problem of dog thefts and the effect they can have on owners.
Mr Johnson said stealing a dog was currently deemed no more serious than stealing other possessions.
"It would be good to have a specific offence of the theft of a pet.
"Too often, the theft of a dog is treated in the same way as the theft of a laptop or a mobile phone," he said.
Ms Oakley added that Dog Lost would like to see custodial sentences.
The Ministry of Justice said: "We are aware of the distress the disappearance of a pet can cause, especially if there are suspicions it has been stolen.
"The maximum penalty for theft is seven years imprisonment and there are no plans to change this.
"The independent Sentencing Council recently issued revised guidelines for dealing with theft which make clear courts should take into account the emotional distress."
How the figures break down across England
See the data for your force area here
Police recorded 4,749 offences involving dogs stolen between 2013 and April 2016. The figures showed a rise of more than a fifth over two years.
They indicate 1,305 offences in 2013, 1,393 in 2014, 1,596 in 2015 and 394 in January - April 2016. Some included more than one dog taken. North Yorkshire Police provided a figure of 61 crimes over the whole period but did not break it down further.
Nottinghamshire Police recorded the highest rate of dog thefts between 2013 and 2016. There were some two dogs stolen per 10,000 people served by the force.
However, Nottinghamshire is one of 10 forces where the number of reported canine thefts has dropped.
In 2013, there were 92 reports of dogs stolen, rising to 94 in 2014. The following year it was 59.
The other forces who recorded a fall compared with their 2013 figures were West Midlands, Durham, Warwickshire, Bedfordshire, Surrey, Cheshire, North Wales and Gwent.
Two other forces, Kent and Devon and Cornwall, had the same number of reports of thefts in 2015 as they did two years previously. A breakdown was not available for North Yorkshire.
Of the 37 forces that responded to the BBC's request , 24 reported more thefts in 2015 than two years earlier. Ten saw a rise in both 2014 and 2015.
Norfolk, Dyfed-Powys, Northamptonshire, Gloucestershire, Hertfordshire, Lancashire, Greater Manchester, Lincolnshire, the Metropolitan Police and West Mercia all saw rises in both years.
Of those, Norfolk and Dyfed-Powys saw the biggest percentage rise, with more than two and a half times the number of reported dog thefts in 2015 compared with 2013.
The number of reported dog thefts has almost doubled in Northamptonshire, up from 14 in 2013 to 27 in 2015.