A consultation has been launched after the government’s initial plan to implement the measure in 2016 was delayed.
Currently, only the businesses themselves are liable for fines of up to £500,000, but the new measure will grant the Information Commissioner’s Office (ICO) the power to hold the boss directly responsible for paying the penalty.
A company is breaking the law if it makes cold calls to people who have subscribed to the Telephone Preference Service – a central opt-out register.
The government hopes the new measure will stop company bosses from avoiding the fines by declaring bankruptcy and setting up the same business under a different name.
The ICO revealed last week it had recovered just over half (54%) of the £17.8m in fines issued for nuisance calls since 2010, as companies go into liquidation to avoid paying.
Digital and creative industries minister Margot James said: “Nuisance calls are a blight on society and we are determined to stamp them out.
“For too long a minority of company directors have escaped justice by liquidating their firms and opening up again under a different name.
“We want to make sure the Information Commissioner has the powers she needs to hold rogue bosses to account and put an end to these unwanted calls.”
The level of fine will be determined on a case-by-case basis, looking at whether it will apply to a company, director, or both.
If a firm has multiple directors, each of them could be liable to pay.
The Insolvency Service can also disqualify people from boardroom positions and failure to adhere to the new ruling could lead to a prison sentence.
ICO deputy commissioner Steve Wood said: “We welcome these proposals from the government to make directors themselves responsible for nuisance marketing.
“We have been calling for a change to the law for a while to deter those who deliberately set out to disrupt people with troublesome calls, texts and emails.
“These proposed changes will increase the tools we have to protect the public.”
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Latest estimates by Ofcom show British consumers received 3.9 billion nuisance calls and texts last year.
The consultation closes in August.