Labour has challenged Health Secretary Jeremy Hunt over the legal basis for dropping a commitment on waiting times.
Shadow health secretary Jon Ashworth has written to Mr Hunt claiming that "the Government and NHS England are acting unlawfully" by accepting that the 18-week target would be missed.
NHS England chief executive Simon Stevens said he expects waiting times to rise slightly as a "trade off" for improvement in other areas, such as hitting the four-hour A&E target and better cancer care.
Longer waits can be expected for pre-planned operations, which include things like hip and knee replacements, cataract removal, hernia operations and laparoscopies.
The NHS target is for 92% of patients to be treated within 18 weeks of referral and Mr Ashworth said "the absolute nature of this legal duty to meet the 92% is reflected in the NHS constitution".
He said: "The NHS constitution isn't just a pledge by politicians, it's a legal guarantee about the standards of care that patients can expect to receive in the English NHS.
"That includes a guarantee to treatment within 18 weeks, which NHS England have now said they can no longer provide because the Government has denied them the funding they need.
"Government ministers need to urgently clarify they are not breaching the NHS constitution and must outline the consequences of denying patients their legal right to treatment within 18 weeks.
"As a first step, the Secretary of State must publish his department's legal advice urgently.
"Earlier this week NHS chiefs announced - without any public consultation or changes to the law - that the NHS will no longer be required to meet the 18-week treatment target because the financial crisis has got so bad. It's utterly unacceptable and a striking admission of how badly the Tories are running the NHS.
"Since Theresa May became Prime Minister standards of care for NHS patients have been in a rapid downward spiral. She might be prepared to ignore NHS staff and the public but she can't just ignore the NHS constitution based on legislation voted upon by Parliament."
On Sky News' Sophy Ridge on Sunday, Mr Ashworth said he thought the NHS needed up to £5 billion extra funding this year - suggesting the Government should scrap tax cuts in order to pay for the health service.
"We can afford the NHS if the Government is prepared to put the money in and make different decisions on tax," he said.
Asked if he was prepared to consider tax increases to fund the NHS, he said: "I am ready to have that discussion with people about how we fund the NHS."
But he added that money was being wasted because of the "privatisation agenda" and a failure to deal with public health problems such as obesity.