Tougher penalties are being considered for nuisance calls and text messages.
Persistent cookie warnings on websites may also be curbed.
The measures are being considered as part of a 10-week consultation on what the government calls the "UK's data landscape", while the Information Commissioner's Office (ICO) is set for an overhaul.
At present, the ICO can fine firms sending nuisance communications up to £500,000.
But ministers would like to align it with General Data Protection Regulation (GDPR), which has a top penalty of £17.5 million or 4% of annual global turnover.
They also want to reduce the number of data protection complaints the ICO deals with each year.
It currently stands at 65,000, but the intention is to focus on bigger cases that could lead to serious harm, rather than more inconsequential ones.
As well as cracking down on abuse, the government wants to "remove unnecessary barriers to responsible data use".
It added: "This can help deliver more agile, effective and efficient public services and further strengthen the UK's position as a science and technology superpower.
"Far from being a barrier to innovation or trade, regulatory certainty and high data protection standards allow businesses and consumers to thrive."
The ICO is expected to get an independent board and chief executive. That would bring it in line with other regulators including the Competition and Markets Authority, Financial Conduct Authority and Ofcom.
Earlier this week, outgoing Information Commissioner Elizabeth Denham urged her G7 counterparts to restrict irritating cookie notices too.
Regarding the review, she said: "People's personal data is used in ever more novel ways; it is right that government looks to ensure a legislative framework that is fit for the future."
Culture Secretary Oliver Dowden said that now the UK has left the EU, it has the "freedom to create a new world-leading data regime".