Four byelections have held the country’s attention in recent months, but a relatively under-the-radar internal Conservative contest that could influence Boris Johnson’s relationship with his restless backbenchers will come to a head on Wednesday, as Sir Graham Brady fights to retain his position as chair of the 1922 Committee. It is not normally a group that makes headlines, but his role grew dramatically in prominence during the Brexit years given the frenzy of blue-on-blue attacks that ended with a Tory prime minister being toppled. Brady’s position is one of the key channels through which Conservatives not on the government payroll can discreetly raise their concerns and fears directly to No 10. With a modernised Conservative party full of younger MPs, including many with little political experience and from parts of the country that have never voted Tory before, Brady’s role as the voice of all backbenchers has been strained. He is being challenged by Heather Wheeler – a former whip and minister – who wants to become the first woman to head the group. Her supporters say Brady does not effectively communicate the width and breadth of Tory MPs’ frustrations – particularly from the 2019 intake – to Downing Street. Her pitch to colleagues is to “reunite the parliamentary party after lockdown” and “work with members new and old to reflect the changing political landscape”. A Wheeler ally said Brady was still likely to win, but he was mostly relying on the support of “old duffers” and was viewed less favourably by the more than 100 Tories who joined the Commons for the first time at the last election. Many view him as “too presidential”, summoning people to his office rather than rubbing shoulders in the tearoom, the source said. Former cabinet minister Andrea Leadsom is said to have made calls drumming up support for Wheeler, and the Guardian understands she is is also backed by a member of the 1922 executive, Sheryll Murray. Other MPs who favour a change from Brady include Jane Hunt, Mark Menzies and John Lamont. Wheeler was not initially the only challenger: Robert Goodwill also sounded out colleagues, but when Brady resisted a system of voting in rounds in favour of a single poll conducted under first-past-the-post, Goodwill pulled out, fearing he would split the vote. While Brady is likely to retain the post he has held since 2010, the challenge underlines some backbenchers’ discontent over their relationship with Johnson. “No 10 don’t care what the 22’s got to say,” one said, gloomily. “Downing Street won’t be swayed by our grumblings – whoever’s conveying the message.” The election, for which Tory MP Charles Walker is acting as the returning officer, ends at 12pm on Wednesday. A result is expected to be announced later in the afternoon.