The vast majority of people say social media firms are not doing enough to tackle online hate.
An exclusive poll for the Mirror found 76% of the public back tougher fines on tech firms that fail to stamp out racism, sexism and abuse.
And 71% say not enough is done to protect young people from online harm and bullies.
The findings will increase pressure on the big social media firms to act.
Football legend Thierry Henry is backing our calls for zero tolerance of online abuse, tougher penalties for firms failing to act and instant bans for those posting offensive material.
It comes as football authorities start a four-day boycott of social media from Friday, in protest at the failure to tackle hatred and abuse.
The Deltapoll survey for the Mirror found 54% believe social media companies are not going far enough to tackle online abuse and bullying.
It also revealed 62% of 18 to 24-year-olds and 53% of 25 to 34-year-olds have been a victim of bullying or harassment.
One in five ) 18 to 24-year-olds and one in seven (14%) 25 to 34-year-olds-year-olds were targeted by trolls in the last month.
1 Zero tolerance of identity-based hate, abuse and bullying on social media.
Firms must remove offensive material that breaches community guidelines immediately. We propose incremental fines for failure to remove such content within a specified time. Firms should also be fined if they fail to remove persistent offenders. Firms must make guidelines more robust and comprehensive.
2All social media firms to have a clear, publicised and accessible mechanism for reporting abuse. Firms should be obliged under law to acknowledge receipt of complaints and explain their action. Social media firms to publish six-monthly reports monitoring abuse and explaining action to eradicate it.
3 Automatic bans for anyone posting offensive material, including lifetime bans for repeated or especially offensive behaviour. Social media firms should explore a system of verification so it is easier to trace, remove and prosecute those spreading hatred.
4 A tax on tech firms to fund educational outreach projects to teach young people about online safety.
5 Demand the Government brings the Online Safety Bill before Parliament now. Make identity-based hate a specific crime alongside child sexual exploitation, inciting terror and promoting violence.
Nationally, a third of people say they or a friend has suffered from online abuse.
Facebook said it “took action” on 26.9 million pieces of hate speech content from last October to December.
Imran Ahmed, of the Centre for Countering Digital Hate, said: “Online harassment and bullying scars people. This is not banter. The Government must listen to the British public.”
Facebook said: “We do not want racist abuse on Facebook or Instagram and we will remove it when we find it.”
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Twitter said: “Abuse and harassment have no place. We have policies in place, applying to every-one, that address threats of violence, abuse and harassment and hateful content. If we identify accounts that violate any of these rules, we’ll take swift enforcement action.”
Deltapoll interviewed 1,590 British adults online on March 31 and April 1. Data is weighted to represent the British adult population as a whole.
- A man appeared in court on Thursday accused of sending West Brom striker Romaine Sawyers an offensive message after a match.
Simon Silwood, 49, of Kingswinford, West Mids, denied the charge before Dudley magistrates and will stand trial in September.