Mr Randall was speaking in the Report Stage of the Police, Crime, Sentencing and Courts Bill in the House of Commons as parliament considered several proposed amendments, including one about a new offence of pet theft.
The MP said: “There has been a lot of organised criminality around the reported rise in pet theft, and I have seen videos posted in local community Facebook groups that show groups of suspicious-looking men looking for dogs.
“Constituents have written to me to say how scared or worried they are when they go out to walk their dog during the day.”
Mr Randall said the price of some dog breeds rose by up to 89% in the first lockdown, and Google searches for “buy a puppy” increased by 166% between March and August after the start of the first lockdown.
The Government launched a Pet Theft Taskforce in May, to look into this issue, and Randall believes they should be allowed to complete their work.
He said: “I believe that legislating now would ignore the work of the pet theft taskforce, which was launched in May. It will try to understand the factors behind the perceived rise in pet theft, recommend measures to tackle that and seek to learn the lessons from related specific thefts, including of mobile phones and metal.”
“We have heard some powerful arguments for tackling the issue. There is more to be done and primary legislation might well be necessary, but I would first like to see the outcome of the taskforce’s review and, if measures are necessary, for that to be backed up with appropriate sentencing.”
The Pet Theft Taskforce will report in the autumn.