Company directors must be “held personally to account” for nuisance calls made by their firms, consumer group Which? said in a statement this week.
The group's research says that since April 2015, 22 fines have been issued to companies for nuisance calls, but only four have been paid in full - something that Which? would like to see change.
Members of the public feel the same way, with 79% of people agreeing that they'd welcome a move to hold senior directors to account.
Director of campaigns and policy Alex Neill said: "Millions of people are still being pestered by nuisance calls and it's time for tougher action that holds responsible company directors personally accountable for the unlawful actions of their companies.
"This will stop rogues stepping around the rules by closing one business and re-establishing a new one, and avoiding fines for making nuisance calls."
The organisation's research also revealed that eight out of 10 people received a nuisance call in May alone - and 40% of them said it made them feel intimidated.
Which? launched its Calling Time on Nuisance Calls and Texts campaign three years ago, which offers a tool for consumers to report nuisance calls they get, and lobbies for more accountability for the companies that make them.
So far, it's got the government to introduce mandatory Caller Line Identification and require tougher fines from the Information Commissioners Office - but in its latest statement, it says far more must still be done to curb the cold callers.