On Thursday’s BBC Politics Live show, the Conservative MP Henry Smith dismissed claims of Islamophobia in the Conservative party, citing the fact he personally had not seen any anti-Muslim discrimination.

Yet we have a fair idea as to just how Islamophobia has taken hold among the party’s support base and how its leadership is responding to such attitudes.

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The latest report from Hope Not Hate gives some indication of where these sentiments may come from. Almost half (49%) of Conservative voters see Islam as a threat to the British way of life, with a similar number (47%) believing the false conspiracy theory that there are no-go areas where sharia law dominates and non-Muslims cannot enter.

Islamophobia and negative attitudes towards Muslims are very much established within sections of British society – where 18% of people believe “Muslim immigration to this country is part of a bigger plan to make Muslims a majority of this country’s population” and 31% of young children believe Muslims are taking over England.

However, the latest statistics split by party preference show that there is a particular tendency for anti-Muslim racists to vote for the Conservative party, over and above others.

While we cannot be certain of the driver, it is noticeable that these sentiments appear at the same time as the Conservative party is being seen to be trying to placate the hard right. Let’s look at one of the statistics – about Stephen Yaxley-Lennon (popularly known as Tommy Robinson), who is described as a far-right Islamophobic extremist by Hope Not Hate.

An unbelievable 42% of Tory voters have a positive view of the way Yaxley-Lennon highlights issues ignored by the media (compared with 18% of Labour voters).

One might have assumed that such a positive view about a widely reviled and hateful figure would not have any place in a modern Conservative party membership.

But the problem seems to be far worse.

The Conservative MP Bob Blackman retweeted an anti-Muslim post from Tommy Robinson, yet he did not even get a slap on the wrist from the party. In fact, depite having subsequently hosted anti-Muslim extremist in parliament (Tapan Ghosh), shared an Islamophobic story on Facebook, and been found as a member of a number of Islamophobic social-media groups, the party seems to have no real concern and the prime minister even chose to campaign with him.

He’s not alone. Conservative MP Nadine Dorries shared a tweet from Tommy Robinson before using far-right tropes against Sadiq Khan, Yasmine Alibhai-Brown and Muslims more generally and – despite being personally against same-sex marriage – weaponised gay rights to attack Muslims. Unlike Blackman, she didn’t even apologise once she was found out.

And I could go on – whether it is Conservative MP Andrew Rosindell’s Facebook account being found to have joined a “Free Tommy” group, or Conservative MPs Jacob Rees-Mogg, Michael Gove and Boris Johnson meeting Steve Bannon, who famously praised Tommy Robinson as representing the working class. Johnson’s burqa comments have led to many claiming that he is using Islamophobia as part of a populist, Trump-like appeal to anti-Muslims in the party.

Yet the party remains silent and believes it can get away with ignoring all those who say that action must be taken, whether it is senior Conservatives, Muslim representative groups, hundreds of mosques across the country, secular groups, women’s groups or national newspapers.

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Islamophobia is not just embedded in attitudes, it also finds expression in policy. For example, the party appears to ignore hate against Muslims in the wider society as well, with its hate crime action plan appearing to have made little progress on issues related to Muslims, quite powerfully demonstrated by the comparatively low funding going to mosques to support security, despite a rise in Islamophobic attacks. There are many who will say this is a clear indication of institutional Islamophobia – if not, how could a mayoral campaign built on racist tropes about Muslims have gained the support of the Conservative leadership, not to mention the active participation of Theresa May and David Cameron? And why would the former chair of the party, Baroness Warsi, say there is a “simmering underbelly of Islamophobia” in the party?

The brilliant work of many Conservatives such as Dominic Grieve, Lord Bourne and James Brokenshire does not detract from the claim of a real and worrying structural problem.

The right way to deal with the monumental weight of evidence would be for the Tories to launch an inquiry into all these accusations in an open, transparent and credible way.

If no action is taken, many more will believe that British Muslims – only 11% of whom appear to have voted Conservative in 2017 – are being ignored as they are electorally insignificant compared to the large numbers of Tory supporters with racist views.

In 2019, surely that is not possible?

• Miqdaad Versi is assistant secretary general of the Muslim Council of Britain