The federal government’s new program to care for elderly Australians at home is so poorly designed it will fuel demand in already overstretched public hospitals and residential facilities, a leading expert has warned.

Kathy Eagar, a former adviser to the aged care royal commission, says delays in expanded services announced earlier this year will exacerbate declining independence and capacity for vulnerable people. It will also increase the risk of falls, medication errors and malnutrition, she said.

But Eagar has told a Senate inquiry considering aged care services that Labor’s new Support at Home program is “fundamentally flawed” and the government’s forecast that it will reduce demand for residential care is not credible.

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Support at Home is replacing exisiting home care packages under changes originally designed to come into force from 1 July.

Eagar said after the new 1 November start date, preventable demand for hospitals and residential facilities will increase.

“Consumer co-payments are too high, assessment is a bottleneck, package wait times post-assessment then create a further bottleneck and there is not sufficient capacity to flex services up and down in response to changing needs,” she said.

“It is inevitable that demand for both public hospitals and residential aged care will increase because the Support at Home program itself is so badly designed.”

The Senate crossbench is pushing Labor to speed up care for the 87,000 people on waitlists.

Eagar has also cast doubt on Labor’s promise to end delays for home care by 2027, reducing maximum wait times to 90 days. She said the ageing population and the proportion of people living beyond 85 will make that promise impossible.

She told an inquiry, set to hold public hearings on Friday, that $17bn in projected budget savings is unrealistic and won’t be achieved.

“They are based on unverified assumptions of the capacity of older people to pay for their care and have not been sufficiently scrutinised.”

The Greens aged care spokesperson, Penny Allman-Payne, is leading the Senate inquiry.

“The longer the community has had to understand these aged care changes, the clearer it becomes they are not going to solve the issues in the system,” she said.

“By November, some 100,000 people will be waiting on a home care package because Labor broke their promise to release care packages in July. At the very least, Labor needs to make good on this.”

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The inquiry follows warnings from the sector that Labor’s changes to residential aged care funding arrangements risk squeezing out elderly people with limited financial means.

Under the new residential rules, wealthier people will be required to pay more for their care, using a payment known as a refundable accommodation deposit (RAD). Elderly people whose care is paid for by the government rely on a supported accommodation supplement, worth $70 per day.

Tracey Burton, the chief executive of Uniting NSW and ACT, told Guardian Australia last month a two-speed system is developing, with the difference in value between payments acting as a strong disincentive for homes to accept supported residents.

The inspector general of aged care, Natalie Siegel-Brown, told the inquiry the delayed start of Support at Home was appropriate, but it was disappointing there was no early release of additional home care packages.

Failing that, Siegel-Brown said new places should be “front-loaded” and made available as soon as possible.

The aged care minister, Sam Rae, told parliament this week demand for in-home care was growing “very, very fast” and promised additional new packages would flow from November.

“The brief deferral of the new Aged Care Act is to ensure that programs like Support at Home are ready for older Australians and their families,” he said.