Leaving the EU could make it easier to push online media companies to take legal responsibility for "persistent, vile and shocking abuse," the official ethics watchdog has said.
The Committee on Standards in Public Life said ministers should legislate to move liability for illegal content onto social media and other internet companies to tackle an "intensely hostile online environment".
Facebook, Twitter and Google "are not simply platforms for the content that others post" because they play a role in shaping what users see, and so "must take more responsibility for illegal material".
They are not liable "largely" due to an EU directive which treats them as "hosts" of online content, but Theresa May's commitment to leaving the single market means the Government can introduce new laws to make companies responsible, the watchdog said.
The report on intimidation in public life, commissioned by the Prime Minister, said social media was "the most significant factor" driving harassment, abuse and intimidation of 2017 General Election candidates, which included threats of violence and sexual violence, as well as damage to property.
"Some have felt the need to disengage entirely from social media because of the abuse they face, and it has put off others who may wish to stand for public office," the report said.
"Not enough has been done. The committee is deeply concerned about the limited engagement of the social media companies in tackling these issues."
Committee chairman Lord Bew said the "increasing scale and intensity of this issue demands a serious response".
"We are not alone in believing that more must be done to combat online behaviour in particular and we have been persuaded that the time has come for the Government to legislate to shift the liability for illegal content online towards social media companies," he said.
The committee was also "deeply concerned" about the failure of Facebook, Twitter and Google to collect data on their processes for reporting and taking down illegal content.
"Their lack of transparency is part of the problem," the report said.
"None of these companies would tell us if they collect this data, and do not set targets for the time taken for reported content to be taken off the platform. This seems extraordinary when their business is data-driven in all other aspects."
The committee urged online companies to put in place automated techniques to identify intimidatory content, while the Government should set up a "trusted flagger" social media reporting team during general elections so abuse and intimidation could be dealt with more quickly.
Lord Bew said: "This level of vile and threatening behaviour, albeit by a minority of people, against those standing for public office is unacceptable in a healthy democracy.
"We cannot get to a point where people are put off standing, retreat from debate, and even fear for their lives as a result of their engagement in politics.
"This is not about protecting elites or stifling debate, it is about ensuring we have a vigorous democracy in which participants engage in a responsible way which recognises others' rights to participate and to hold different points of view."
The report also called for "greater energy and action" from political parties, Parliament, the police and traditional media, as well as MPs and candidates themselves, warning: "This is all the more important in the light of recent allegations of sexual harassment and bullying in Parliament which will have shaken public confidence in politicians."
Among other recommendations, ministers should consider introducing a new offence in electoral law of intimidating parliamentary candidates and party campaigners.
And police forces should be given better guidance and training on the context in which MPs and candidates operate and the nature of social media technologies.
The committee said leaders of political parties should "always call out intimidatory behaviour" even if it is perpetrated by those on the fringes of their party.
Parties must also produce joint codes of conduct on abuse and intimidation during election campaigns by December 2018, which will be jointly enforced.
The committee said it was also concerned about the impact on the diversity of a representative democracy and said parties have an "important responsibility" to support female, black and minority ethnic and LGBT candidates.