James Frayne is Director of communications agency Public First and author of Meet the People, a guide to moving public opinion. The focus of this column is Theresa May’s conservatism for “ordinary working people”.

Theresa May treads a difficult line on security. As Prime Minister, she must speak for the country – echoing public sorrow for the lost and damaged lives of the victims, and setting out a robust policy response from Government. It’s vital politicians retain public consent for their approach to potentially divisive issues, and they must understand the public mood as they speak and form policy. So where does the public stand?

These days, analysing public opinion is complex because social media plays such a prominent role in public discourse. But as we know from both 2015’s General Election and the EU Referendum, there’s often a big gap between what’s visible on social media and what’s really in people’s hearts and minds. However, there are significant amounts of data available that allow us to piece together the public mood. From this we can draw several key conclusions.

First, it isn’t possible to be too tough on terrorists. The public want and expect a brutal response to terrorists who operate on the streets of Britain or who threaten British lives from abroad. People think the death penalty should be reintroduced for convicted terrorists and they have traditionally supported the police’s use of “shoot-to-kill”. They supported the killing of so-called “Jihadi John” in the US/UK drone strike in massive numbers. They also think those returning from Syria who are suspected of fighting for ISIS should have their passports removed.

Secondly, the public are prepared to extend significant powers to the intelligence services to track terrorists. People think they should be given practically any new powers they need and they have great confidence in their integrity and competence. This extends to the police but to a slightly lesser extent; there is some concern the police might misuse powers given to them. To the extent that they see it as a choice, the public put security far ahead of privacy in regards to intercepting electronic communications.

Thirdly, and crucially, while they’re clear on what should be done with actual terrorists, the public are unsure about what longer-term action to take to deal with extremism. They reject broadly-focused cultural policies targeted at Muslims: there was recently very little enthusiasm for Trump’s proposed travel ban and little support for a ban on refugees arriving from places like Syria. While the public admits concern about the future role of Islam in the UK, people accept most Muslims are peaceful and report positive interactions with Muslims on a personal level.

This lack of clarity on what is obviously a complex policy challenge means that there is widespread sympathy (but not universal support) for withdrawal from the ECHR and a strong belief that human rights laws are being abused. There is also widespread support for a crackdown on extremist preachers using the web, but some doubt as to whether this will really solve the problem.

For politicians, all this in turn means three things. Firstly, that they must take no risks at all with security – ensuring that the police, intelligence agencies and military have all the resources they need and that they are deployed to use lethal force without hesitation. Secondly, that they should not worry that the public is shifting towards aggressive, populist cultural policies targeted at Muslims. They aren’t, and politicians don’t need to pander to such demands. Thirdly, it means politicians must start talking about counter-extremism policies to the public at large. People want to know that the Government are actually doing things and they want to know what politicians think will work best. They are open-minded about policies Governments pursue, but they want to know something serious is being done.