As federal and state governments unveil millions of additional dollars for mental health during the coronavirus pandemic, experts warn many still face an uphill battle to access services, with “far more people needing support and services than there are people to provide them”.

The latest funding injection came on Monday when the federal government announced $31.9m of additional support, specifically for Victoria, where stage-four restrictions will remain in place at least until 13 September.

However, many people are being forced to wait for weeks or months, a situation worsened by the pandemic creating a surge in demand.

Mental health experts and bodies in Victoria have welcomed the commitments – noting also an earlier federal pledge to double the number of Medicare subsidised mental health sessions to 20 – but point to a system so dysfunctional and fragmented it was already the subject of a state royal commission.

With the state still under harsh stage-four restrictions, politicians have acknowledged the probable impact of six weeks where Melburnians can go out to exercise only 60 minutes a day, cannot travel beyond 5km of their home, and most of the economy is shut.

A key concern is what is often called the “missing middle”, those who fall between the gaps. It includes people who need more help than they can access, but have not yet reached a level of distress that would require going to hospital.

“It is a growing middle sector because of the external environmental stressors that are going on at the moment,” said Prof Jayashri Kulkarni, director of the Monash Alfred psychiatry research centre.

Helplines such as Lifeline and Beyond Blue were “relatively easy to access” and had rightly received extra funding during the crisis, Kulkarni said.

Yet in general the opposite is true of access to a mental health clinician. Some experts say practitioners are often concentrated in wealthier suburbs or charge fees people cannot afford. Bulk billing practices are not widespread.

People can face long waiting times for counselling services, may be ineligible to access support at a community clinic, or be unable to afford – or struggle to find – a private practitioner.

Although some of the slack is picked up by GPs, the situation has got worse as demand for mental health care increased during the pandemic.

“The issue now is that simply there are far more people needing support and services than there are people to provide them in the private sector,” said Dr Kerryn Rubin, Victorian branch chair of the Royal Australian and New Zealand college of psychiatrists.

“So even people who previously would have accessed the private sector are struggling to do that because they can’t get an appointment for four, eight, 12 weeks, at which point in time often something that started off as a minor or moderate problem becomes a severe problem.”

Figures released earlier this month by the Victorian government showed a 33% increase in people under 18 being treated in emergency departments for intentional self-harm. The overall rate was also up 9.3%. Statistics from Beyond Blue showed calls to the service were up 47% in June compared with the previous year, Guardian Australia reported last month.

Kulkarni said the lockdowns had exacerbated depression and anxiety but the nature of the pandemic meant practitioners were also seeing more cases of obsessive compulsive disorder.

Peter Baldwin, a clinical research fellow at the Black Dog Institute, also works as clinical psychologist in OCD, trauma and hoarding.

“People who treat hoarding disorder are pretty rare, so demand is pretty high,” he said. “But I’ve noticed I’ve gotten a lot of referrals … There’s this link between what’s been going on in the pandemic, and people acquiring things and that becoming more and more of a problem for them.”

Kulkarni, Baldwin and Rubin all said that even as experienced practitioners they found it incredibly difficult to find referrals for patients they could not see themselves.

“Sometimes it is a bit of luck of the draw,” Baldwin said. “When people come to me and I can’t see them, I find it really difficult to find someone else who can see them. And that’s me as a practitioner inside the system.”

Rubin said he had recently sought to facilitate a referral for somebody and found the “first eight psychiatrists I spoke to said: ‘We’re really sorry but we just don’t have the capacity to pick anyone else up.’ ’”

Like Baldwin, Rubin emphasised that “that’s ringing around as a professional”.

The experts welcomed the federal decision earlier this month to double the number of Medicare-subsidised mental health sessions to 20. But were they were concerned some – especially those seeking mental health services for the first time – would be locked out.

“We don’t know how that’s going to impact it if everybody then just keeps the same patients going for 20 sessions rather than having more availability,” said Kulkarni.

Baldwin said: “Having more money to pay a psychiatrist or psychologist doesn’t mean there are more psychologists and psychiatrists to pay.”

On Monday the federal health minister, Greg Hunt, said the commonwealth’s latest funding package would include 15 adult mental health centres that would be set up “over the course of the coming weeks” across Victoria.

It came only days after Victoria’s $60m funding boost. Much of that went to mental health inpatient beds, but initiatives also included extending opening hours of community-based mental health services.

Rubin said that was particularly welcome: “One of the huge issues with the current community mental health system is it is Monday to Friday, nine to five.”

• Crisis support services can be reached 24 hours a day: Lifeline 13 11 14; Suicide Call Back Service 1300 659 467; Kids Helpline 1800 55 1800; MensLine Australia 1300 78 99 78; Beyond Blue 1300 22 4636