Rishi Sunak has refused to say whether he uses private healthcare amid suggestions he is out of touch with millions of ordinary people who face long waiting times to receive treatment on the NHS. The prime minister said his own healthcare was “not really relevant” and was a “distraction” from his focus on making sure people across England receive high-quality NHS provision. However, he faced criticism from Labour for giving the impression of being a leader who “not only doesn’t use the NHS but doesn’t understand the scale of the challenges” it faces. Health workers’ unions urged him to “come clean” over his provision. The Guardian revealed in November that Sunak was registered with a private GP practice that guarantees that all patients with urgent concerns about their health will be seen “on the day”. NHS England figures show most patients have to wait longer for an appointment. The west London clinic used by the prime minister charges £250 for a half-hour consultation and, unlike most NHS GPs across the country, offers appointments in the evenings and at weekends, as well as consultations by email or phone that cost up to £150. Sunak has made reducing NHS waiting lists one of his key priorities over the next two years and has held emergency talks with health leaders to alleviate the crisis. But under sustained questioning from the BBC’s Laura Kuenssberg, he refused to say whether he had used private healthcare to avoid queues himself. “As a general policy I wouldn’t ever talk about me or my family’s healthcare situation,” he said. “But it’s not really relevant, what’s relevant is the difference I can make to the country.” He said healthcare was a “private” matter, adding that discussing his own situation was “a distraction from what the real issue is, and the real issue is are we making sure there’s high-quality healthcare for the country”. He added: “But when it comes to the private sector in general, we should be making use of the independent sector. I don’t have any problem with that whatsoever.” The Royal College of Nursing general secretary, Pat Cullen, who has been leading strikes in an attempt to secure a better pay deal for nurses, told the BBC: “I think as a public servant, you ought to be clear with the public whether or not you are using private health cover. “That’s about being open, it’s about being transparent, and it’s about honesty. I think he needed to come clean. As a public servant he is elected by the public, so he is accountable to the public, and when you’re accountable to the public, you have to be honest with them.” The shadow health secretary, Wes Streeting, who said he does not use private healthcare, sought to paint Sunak as being out of touch. “I thought the prime minister in that interview gave the impression of someone who not only doesn’t use the NHS but doesn’t understand the scale of the challenges or have a plan to deal with the fundamental problems,” the Labour MP told the BBC. “Because, yes, you can get people around the table in No 10 for a photo op, yes you can do more sticking plasters to get through this winter … But we need fundamental change in the NHS to deal with what is the biggest crisis in its history.”