The prime minister has chosen to mark the centenary of women’s suffrage with a call for greater protection for MPs and others against abuse. She announced today that the government would consult on making the abuse of MPs a criminal offence. As someone with more than enough experience of personal abuse and threats, in my judgment this is a thoroughly misguided intervention, and Theresa May should have a rethink.

It is unclear why MPs or other elected representatives should have special treatment in law to protect them. There are already laws against violence, threats, intimidation, harassment and stalking. But the experience of victims shows that the law is too often a dead letter. It is only when the situation has escalated beyond control that there is effective police intervention.

No one in public life should ever diminish the real risks that exist. The brutal terrorist murder of one of our own, Jo Cox MP, should put paid to any complacency. Numerous other politicians have also faced lethal threats and extreme violence. We do need safeguards. But so do the public.

Why is the prime minister so insistent on this misconceived course of action?

In this country, approximately two women a week are murdered in England and Wales, usually by men known to them, and often by partners and ex-partners. There were five major terrorist incidents in the UK last year in which dozens were killed and many more seriously injured. The police report that violent crime, including knife crime, gun crime and sexual assault, is on the rise. All of these victims and potential victims deserve protection.

But murder, terrorism and crimes of violence are already illegal. The prime minister has failed to identify any new category of offence that is not currently illegal. Instead, she is focusing on a tiny new category of victims, and seeking to privilege their protection over the safety and security of all our citizens. In a democracy, we must all have the right to protection from crime, not just an elite. The sole new effective measure, the withholding of councillors’ home addresses, seems justified. But this could be achieved through a statutory instrument and does not require a new act of parliament.

There is an area where the prime minister could act, but is failing to do so. The internet and social media are now almost indispensable tools of everyday life. But they have opened up the opportunity for trolls, abusers and the genuinely dangerous to vent at the click of a button. Just as newspapers and publishers are obliged to moderate content to block illegal content, so internet giants should be obliged to do the same.

Instead, the prime minister proposes the equivalent of a fireside chat with internet executives. It is not an approach that works. The internet is the new battleground against abuse and threats of violence, and it is the one new area that merits new legislation that would force the Googles, Facebooks, Twitters and others to act.

Women's suffrage centenary: May pledges consultation on criminalising abuse of MPs - at it happened Read more

Why is the prime minister so insistent on this misconceived course of action? The short answer is that this government typically attempts to legislate away social problems. It lacks the will to tackle genuine problems, and has cut the resources that are required to do so.

More legislation against violence and harassment is not the answer. The real issue is an overstretched police service. Policing, along with the NHS, has become the public service of last resort in austerity Britain. Everything, from mental health problems, to homelessness, to lack of drug services lands at their door.

Yet the Tories have cut 21,000 police officers. Ask any police chief whether this has compromised their ability to fight crime and you will get a very blunt answer. Even as the police record more crime, including violent crime, the number of charges or summonses has fallen under the Tories.

More protection is needed, especially against violent crime and threats of violence. But it’s everyone who needs that protection, not just MPs. Internet companies should be compelled to act against online criminals. But our laws become redundant if there aren’t the police to enforce them.

• Diane Abbott is MP for Hackney North and Stoke Newington