Rishi Sunak refused to say whether he uses private healthcare as Brits struggle with long waiting lists to see GPs and receive treatment.
In a BBC interview on Sunday, he said that it was “not really relevant” whether he would be prepared to pay for faster treatment.
The Prime Minister also raised a glimmer of hope that future nursing strikes could be averted by saying he was willing to discuss pay, but indicated he would not negotiate over the current deal.
Royal College of Nursing (RCN) general secretary Pat Cullen said she had a “chink of optimism” after noticing a “little shift” in the Prime Minister’s stance on Sunday.
Sunak declined to describe the NHS as being in crisis, but admitted it was “undeniably under enormous pressure”.
Ms Cullen will be among the union leaders meeting Steve Barclay for talks on Monday, but the UK Government’s health secretary wants to focus negotiations on a new pay deal for 2023/24.
The RCN head has urged ministers to meet nurses halfway on their pay rise demands for the current financial year and will strike in England on January 18 and 19 without a breakthrough.
The Prime Minister told the BBC’s Sunday With Laura Kuenssberg programme that Monday’s talks are “really important” but he indicated only the next financial year’s pay is up for discussion.
“When it comes to pay we’ve always said we want to talk about things that are reasonable, that are affordable and responsible for the country,” Sunak said.
“We are about to start a new pay settlement round for this year, we’re about to start that independent process, and before that process starts the Government is keen to sit down with the unions and talk about pay and make sure they understand where we’re coming from.”
Ms Cullen told Sunak to “grasp the nettle, come to the table” as she indicated cautious hopes for resolving the long-running dispute.
She told the BBC: “When I listened to that there was a chink of optimism and there was a little shift in what the Prime Minister was saying.”
However, she added of his comments: “This is not about negotiations tomorrow, it’s not about nurses’ pay and it’s not addressing the issues that are our dispute and that is addressing pay in 2022/23.”