Rishi Sunak’s team is being urged to overhaul his “general election-style” campaign in favour of a grassroots effort speaking directly to Tory members in a last-ditch attempt to beat Liz Truss to the Conservative leadership.

With some supporters of the former chancellor in despair over the apparent grip Truss has assumed over the contest to replace Boris Johnson, allies have warned that there has been too much focus on polished social media content, TV appearances and visits to swing voters that have not won over Tory members.

Many Conservative MPs believe there is now only a brief window to change the race, with ballot papers delivered to members from . Some prominent backers want Sunak and a large network of supportive MPs to dedicate their time solely to contacting local members directly through phone banks and online group calls to make his case.

Truss attempted to play down suggestions that she was on course for a clear victory on Saturday, stating that the race to become prime minister “is not finished”. Despite endorsements from prominent Tories in the past week, she said it “would be extremely premature” to start thinking about who would have a place in her cabinet. She added: “This is a very, very close race, and I am fighting for every vote.”

Several MPs said that many local members had been relatively easy to persuade to back Sunak over Truss once they had been contacted, arguing that support for the foreign secretary was often soft. However, they said that the “air war” aspects of Sunak’s campaign were simply not reaching the membership, thought to comprise around 160,000 people.

“They’re running it like an election campaign,” said one Sunak backer. “This is very straightforward. There’s 160,000 Tory members dotted around the country. We know who they are. We know where they are. All we have to do is talk to them. The social media campaign, the TV appearances – most of them make no difference to members.

“The vote is very soft, you don’t have to do much to move it. We’re making this far too complicated. There’s brilliant people in charge, but I’m just worried we’re fighting the wrong campaign.”

Another MP said: “The stuff they have their guys producing is social media stuff for a general election. This is about party members. It should just be about getting Rishi and key supporters to as many members as possible. They are trying to get MPs out for them, but it’s mainly producing social media graphics.”

A third ally said: “I do think it’s looking quite difficult for him but I can’t give up hope yet. There are a lot of MPs talking to their associations. There’s still time. It would be preposterous to just go through the motions for the next four weeks.”

Campaign sources said last night that Sunak was already heavily engaged in talking directly with members, including via online calls and local events. They said that regional campaign coordinators had been working with supportive MPs from the start to reach members. He was also photographed meeting groups of members yesterday.

“The more people see Rishi, the more they like him, so our strategy is getting him in front of as many members as possible,” said a campaign source. “We are undeniably the underdog, but last time I checked Brits quite like the plucky underdog coming through. Members don’t like being told what to think by the media, so Team Truss shouldn’t count their chickens just yet.”

Liz Truss yesterday; a series of prominent Tories have swung behind her in the past few days.

His team described yesterday as “super Saturday”, targeting local Tory associations in key southern constituencies with large memberships. They are also areas where members are more likely to have been upset by the chaotic nature of Johnson’s premiership.

There continue to be concerns over how the party will come back together after a bitter campaign. Amanda Milling, the foreign office minister and former party chair, is pressing the candidates to sign up to a “clean campaign” pledge to limit the damage. “This leadership race has been the most toxic I have ever seen,” she said.

“For the remainder of the race, I call on the teams to stop the blue on blue and focus on a clean, fair and policy-focused campaign. If we don’t, we make the task of reuniting the party harder and risk seeing us out of power for a decade.”

Polls of Tory members have suggested Truss has a healthy double-digit lead over Sunak, but the former chancellor’s cheerleaders say the battle is not over. “The sense is that the vote for Truss is still soft, and so we shouldn’t assume anything about the members just yet,” said an insider.

To make an impression on the race, Sunak announced last night plans to charge patients £10 for a missed medical appointment to help clear the Covid backlog. He said he would revive high streets, slash the number of empty shops and backed tougher punishment for graffiti and littering, as well as additional powers for police to tackle anti-social behaviour.

“I understand the vital role that high streets play in local communities. I don’t just want them to survive; I want them to thrive,” he said. “We should all take pride in our high streets so I will also crack down on anti-social behaviour, graffiti and littering – through extended police powers and increased fines. I have been clear that I have a plan to rebuild our economy; our high streets are a crucial part of that.”

In an earlier intervention Sunak vowed to tackle what he described as “woke nonsense”. While claiming he had no interest in fighting a “culture war”, he said he wanted to “end the brainwashing, the vandalism and the finger pointing”. It led to accusations that he was trying to outflank Truss on the right.

The pleas for a campaign overhaul are a sign of frustration and anxiety among Sunak supporters. As Sunak trails Truss in the polls, a series of prominent Tories have swung behind the foreign secretary in the past few days as she has consolidated her status as frontrunner.

Tom Tugendhat, who had emerged as the preferred leadership candidate of the centrist one-nation wing of the party, is the most recent major figure to endorse Truss. He said that her plan for immediate tax cuts was “founded on true Conservative principles”.

His support followed endorsements from Jake Berry, the influential leader of the Northern Research Group of MPs, and defence secretary Ben Wallace, a favourite among Tory members.