Figures obtained under the Freedom of Information Act show a 22.6 percent rise in reports in two years, reports the BBC.
Calls for a specific crime of pet theft have been introduced by Gareth Johnson, Conservative MP in Kent.
Figures showed at least 5,188 dogs have been reported stolen since 2013.
They indicate 1,454 taken in 2013, 1,577 in 2014, 1,739 in 2015. In the first four months of this year, there were a reported 418 offences.
Some forces reported the theft of several dogs at the same time as a single offence.
Breeds targeted include popular celebrity dogs such as French bulldogs and pugs, as well as Staffordshire bull terriers.
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.