A cross-party campaign calling for an NHS and Care Convention got its "foot in the door" when the group of MPs held talks with Theresa May in the House of Commons on Wednesday (1 February).
Liberal Democrat Norman Lamb, a former care minister, told IBTimes UK that the discussion with the prime minister and Health Secretary Jeremy Hunt was "very constructive".
Lamb was joined by two senior Labour MPs, Meg Hillier and Frank Field, and three top Conservatives, Hugo Swire, Sarah Wollaston and Dan Poulter.
The group want to establish the NHS and Care Convention to find a long-term solution to the "crisis" in health and social care funding.
"It was very constructive and I'm pleased that the prime minister agreed to speak to us," Lamb said.
"They took us seriously, they took the case we made seriously and we asked if [May] was willing to initiate a dialogue to explore this idea further, rather than slamming the door on us, and she did that."
Lamb said the group will next meet with the prime minister's newly appointed health adviser, James Kent. "I don't know where this will lead to, I don't know whether we will achieve a breakthrough, but it must be worth trying – it's better than us shouting at each other," he added.
The government claims it is investing an extra £10bn ($12.6bn) in NHS England, £2bn more than the health service asked for in 2014. But the figures have been disputed, notably by NHS England chief executive Simon Stevens.
He told the Public Accounts Committee, which is chaired by Hillier, that his £8bn funding plan related to a five-year-period, while the government's £10bn commitment covers six years.
"I don't think that's the same as saying we're getting more than we asked for over five years because it was a five-year forward view," he told the MPs.
The British Red Cross charity has also claimed that NHS England is facing a "humanitarian crisis" in its hospitals, a warning which May branded as "overblown".