LONDON — After enduring months of criticism over his bold proposal to drastically overhaul Britain’s publicly financed National Health Service, Prime Minister David Cameron on Tuesday released a new, watered-down version of the plan designed to be more palatable to interest groups and to Parliament.

The opposition Labour Party seized on the chance to accuse Mr. Cameron of making an embarrassing U-turn on a cherished policy. But the prime minister said that on the contrary, the new proposal showed that his Conservative-led coalition government was flexible and willing to modify its programs when the occasion called for it.

“We have listened, we have learned, and we are improving our plans for the N.H.S.,” Mr. Cameron said as he unveiled the new proposal at Guy’s Hospital in London. “We come here today with a substantive package of changes.”

But he said the basics of the plan — “more control to patients, more power to doctors and nurses, less bureaucracy in the N.H.S.” — remained the same.