If you ever wondered why we live in a country where politicians are less trusted than estate agents, look no further than our own prime minister. Earlier this month, the Conservative party was running the most tawdry, bigoted campaign in a generation, and David Cameron was at its absolute heart. Zac Goldsmith has rightly been disgraced for his desperate attempt to secure London’s City Hall by smearing Sadiq Khan, suggesting links to extremists and terrorist sympathisers. But the absolute nadir of this unforgivable campaign was when Cameron hid behind parliamentary privilege to falsely smear Suliman Gani – a British citizen – as an Islamic State supporter, and link him to Khan. That Gani was a Conservative supporter who had repeatedly shared a platform with members of Cameron’s own party, and who had fallen out with Khan over his support for equal marriage, was of no consequence. Here was a cowardly attempt to tap into the most base prejudices that exist about Muslims.

Just weeks after London rejected this poison, Cameron shared a platform to campaign for Britain’s EU membership with a man he had insinuated was a fellow traveller with extremists. “In one generation someone who is a proud Muslim, a proud Brit and a proud Londoner can become mayor of the greatest city on earth,” he serenaded Khan. “That says something about our country.” The British lexicon would benefit from a word that combines “shameless” and “nauseating”. Cameron did his utmost to prevent this “proud Muslim” from assuming office, not by aiming legitimate fire at policy differences, but by portraying a man who received death threats for voting for LGBT civil rights as an associate of Muslim extremists. By doing so, he sent a powerful – and destructive – message to British Muslims: that even a progressive Muslim who rails against the “cancer” of extremism is unfit for public office.

And we wonder why there is such widespread cynicism and contempt for Britain’s political elite. It would be bad enough if Cameron believed Khan was a genuine threat. He clearly did not because while he is shameless, he is not stupid. He simply recognised that fanning dangerous prejudices about a prominent Muslim was a means to a political end. Now he is fighting for his political life in the EU referendum, he celebrates what it says about our country that a “proud Muslim can become mayor of the greatest city on Earth”.

Some will ask: who am I to be offended on Khan’s behalf? He was the target, after all, not me. He has risen above it, put aside the vitriol thrown at him for the greater good. It is his own decision to share a platform with Cameron, even though the lesson of the Scottish referendum was surely that Labour figures joining forces with senior Tories repels Labour voters and cements the idea of an establishment stitch-up. But politicians cynically undermining social cohesion and exploiting prejudices for political gain should concern us all. The entire episode shows how disingenuous and dishonest our prime minister is. I have no sympathy for the official leave campaign, currently running its own fear campaign centred on migrants. But when critics point out that Cameron – just months ago – said he was prepared to leave the EU, and now issues apocalyptic threats of a third world war if Britain votes for exit, it is difficult not to conclude that here is a man who will say anything for political gain. That doesn’t just damage Cameron. It damages people’s faith in politics as a vehicle for change, and undermines people’s faith in democracy. We all suffer for it.