Video report by ITV News National Editor Allegra Stratton
The head of NHS England has called for the Brexit campaign's pledge leaving the EU would mean more money for the health service to be honoured.
Simon Stevens said that failing to do will risk voters losing trust in politics as he warned current funding is "well short of what is needed".
Mr Stevens also said the NHS waiting list will soar to five million by 2021 unless the service is given more money.
"That's an extra million people on the waiting list. One in 10 of us waiting for an operation - the highest number ever."
On current levels of funding, improvements in cancer care or mental health would also not be possible, he added.
Mr Stevens cited the Leave campaign's controversial claim that Brexit will bring £350 million back under British control to spend on the NHS.
He did not call specifically for the figure that was emblazoned on the side of the Vote Leave bus used by key Brexiteers in the run up to the referendum.
But he insisted trust in democracy "will not be strengthened" if Chancellor Philip Hammond argues in his forthcoming Budget that economic instability caused by Brexit means he cannot promise extra cash for the NHS.
Speaking at the NHS Providers conference in Birmingham, Mr Stevens said: "The NHS wasn't on the ballot paper, but it was on the Battle Bus. Vote Leave for a better funded health service - £350 million a week."
He also quoted Vote Leave campaign director Dominic Cummings' analysis that Britain would have voted to Remain in the EU without the pledge.
"Rather than our criticising these clear Brexit funding commitments to NHS patients - promises entered into by Cabinet ministers and by MPs - the public want to see them honoured," he added.
"By the end of the NHS's next financial year - March 2019 - the United Kingdom will have left the European Union.
"Trust in democratic politics will not be strengthened if anyone now tries to argue: 'You voted Brexit, partly for a better funded health service. But precisely because of Brexit, you now can't have one.'
Mr Steven's speech comes as leading health think-tanks warn that NHS the needs £4 billion in 2018/2019 to prevent patient care from deteriorating.
The Health Foundation, The King's Fund and the Nuffield Trust carried out as joint analysis of NHS finances in England and say funding will be at one of the lowest rates in its history next year.