THERESA May has been forced to issue a defiant response to Tory backbenchers who have questioned her future as Conservative leader, declaring: “I’m not a quitter.”

After a week of turmoil and mounting speculation about possible challenges to her position, the Prime Minister insisted that she was getting on with the job of delivering on the real-life issues which matter.

May admitted that there was “always more for us to do” on issues such as housing and schools and appeared to acknowledge that she had not done enough to get her message across to voters.

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But, in a message apparently directed at grumbling Conservative MPs, she said her party should “speak out more loudly about the Government’s achievements”.

Asked by reporters travelling with her on a trade mission to China whether she expected to lead the Tories into the next election, May said: “First and foremost, I’m serving my country and my party. I’m not a quitter and there’s a long-term job to be done.

“That job is about getting the best Brexit deal, it’s about ensuring that we take back control of our money, our laws, our borders, that we can sign trade deals around the rest of the world. But it’s also about our domestic agenda.”

Responding to former minister Robert Halfon’s suggestion at the weekend that she had governed like a tortoise when a lion was needed, May retorted: “I have never tried to compare myself to any animal, or bird, or car, or whatever comparisons that sometimes people use.

“There’s a focus to the Government. Yes, we want to get Brexit right and we are working on that, but we also alongside that are working on the key issues that matter to people on a day-to-day basis.”

May steered clear of direct criticism of backbenchers who have accused her of lacking drive and publicly described her agenda as “dull”.

But she pointedly added: “We need to ensure that we do speak about the achievements that we’ve seen.”

She cited a reduction of unemployment to its lowest level since 1975, a cut in the educational attainment gap between children from rich and poor backgrounds, stamp duty relief for first-time buyers and GDP growth.

“If you look at what, as Conservatives in government, we’ve achieved in terms of national minimum wage increases, the lowest unemployment since 1975, what we’ve done in school attainment with 1.9 million more children in good or outstanding schools – all of these things make a big difference to people’s lives on a day-to-day basis,” she said.

“That’s what people raise when you go on the doorsteps and talk to people. It’s those issues that matter to them and that’s what we are delivering on.”

“Is there more for us to do, to talk to people about what we are achieving and what we are doing? Yes, there’s always more, to talk to people about what we are achieving.

“Sometimes (Tory MPs) say ‘1.9 million more children in good and outstanding schools, but we need to go further’. Yes, of course we do, and that’s what we are doing.”

Pushed on whether she would fight to keep her job if disgruntled Tory MPs forced a vote of no confidence, May said: “You always like talking about hypothetical situations. Let’s talk about now and what we are doing now.”

She also brushed off suggestions Conservative leadership rules – which require the chair of the backbench 1922 Committee Sir Graham Brady to call a vote when he has received 48 letters from MPs – leave doubt hanging over the future of a serving prime minister.

“The rules are set are a matter for the party,” she said. “We are in government. The next General Election isn’t until 2022.”