Demand for services was growing at a higher rate than the population and they had reached the limit.
"It is important that the committee knows that the system in Auckland is under stress," he said.
"The story of Auckland is a story about growth. Last year Auckland grew by the population of Nelson," Levy said.
"And there is very little resilience, if any, in the system. The last year has taken us to the limit."
Levy also questioned whether the public health system was sufficiently resourced to deal with a pandemic.
The health executives were far more blunt that usual because they are effectively between government budgets.
They were speaking about the effects of funding from a previous government and were pleading their case for a big share of the $8 billion extra in health spending promised by Labour over the next four years.
Population growth
Levy said that in the past five years the population had grown at 9.4 per cent but emergency department attendances had increased 18.8 per cent; in-patient discharges by 15 per cent; and spending on services for older people by 14.4 per cent.
The population of people aged over 65 was going to double in the next 20 years. If Auckland grew at medium projections over the next 20 years there would be 560,000 more people; if it grew at high projections, as it had been doing, there would be 780,000 more people in 20 years.
Waitemata District Health Board chief executive Dale Bramley said the three boards had reached new peaks of emergency department attendances that would normally occur in winter.
He also talked about bids for three capital projects that were before the Ministry of Health capital committee.
One included a $500 million upgrade at North Shore where some wards had six patients to a room.
'No longer managing'
Counties Manukau chief executive Gloria Johnson said levels of demand were "so unprecedented and so extreme that we are actually no longer managing".
"We really became aware of it over the summer of 2016 -17 when acute surgical demand peaked then failed to drop off.
"That meant our services were already overstretched by the time we got into winter.
"Our medical demands during the winter were extreme."
The DHB had periods when on every week day the acute beds were running at 120 per cent occupancy.
Johnson said that meant they were having to open areas for beds not intended to have them.
The demand this summer had been greater than last summer.
Speaking about proposal for capital expenditure, Levy said many of the problems were not new.
"We have been facing this for years and every year make savings or defer capital or struggle to get permission to get capital through the [Ministry of Health] capital investment committee."
Decision-making was too slow, he said.