Eleven children were transferred off Nauru to Australia on Monday, a Senate estimates hearing has been told, amid growing calls for all refugee children and families to be removed from the island.

It brings the the number of children brought to Australia to 29 in just one week, leaving 55 still on Nauru.

The Department of Home Affairs also revealed it has spent almost half a million dollars in legal fees in three months responding to court applications for urgent medical transfers of asylum seekers and refugees on Nauru.

The amount revealed on Monday afternoon eclipses the total for the entire previous year, and applies to about 37 cases – sometimes involving multiple people – brought to court since 1 July.

A growing number of critically ill people held on Nauru have sought legal intervention to access required healthcare unavailable on Nauru. Eleven children were transferred to Australia on Monday, while another 3 or 4 children were transferred over the weekend.

The children – who range in age from an infant to 17 years – are among 12 families transferred since Sunday, and 23 since last Monday, the Asylum Seeker Resource Centre told Guardian Australia.

Of the 23 family groups, which includes young adult children, eight were brought to Australia under federal court order, six were the result of legal intervention but the government conceded before it reached court, and just eight were at the initiative of the Australian Border Force.

At least one involved an air ambulance transfer.

The department’s first assistant secretary, Pip De Veau, also revealed the total cost of responding to such applications in the first quarter of 2018-19 was approximately $480,000.

The funds covered external legal providers and counsel, and did not include costs orders.

Last month Guardian Australia reported the government had spent $326,000 last financial year, with widespread expectations that it would be far more this year.

However, on Monday that figure was given as $275,000, and a total amount across the two financial years of about $780,000. Guardian Australia sought clarification and was told the original figure of $326,000 was an error.

The rising costs are caused by an increase in the number of cases brought to court, from seven in the months of May to August, up to 19 in September alone. There have been 16 since the beginning of this month, but De Veau said there were another one or two in recent days that may not be counted in the data.

Of the cases since May, there have been 36 court orders, four that reflect ministerial undertakings, and four cases where no orders were given, she said.

“The orders have varied; sometimes the orders are relating to the provision of certain medical care and are not specific as to where,” De Veau said.

Some others specified Australia, while others included specific hospitals and doctors, she added.

Guardian Australia has reported on cases that included the subject be transferred with family members to specific hospitals or – in at least one case – specifically not by anyone connected to Australian Border Force or its health contractor IHMS.

The secretary of the Department of Home Affairs, Michael Pezzullo, didn’t recall any cases relating to people in onshore detention.

The cases have been brought by Australian-based legal firms, representing clients on Nauru who have in many cases been recommended for medical transfer repeatedly, sometimes for months or years.

They include a large number of children, among whom there is a worsening mental health crisis and several cases of resignation syndrome – a rare and potentially fatal condition that is considered a reaction to extreme trauma.

Dr Parbodh Gogna, the recently appointed chief medical officer for ABF, told the estimates hearing ABF would sometimes have no notice of the court applications, when they would then look at the evidence and approve a transfer.

Gogna said he had visited Nauru once since starting the role, but did not see any detainees “in a consulting format”.

He said there was an “unprecedented jump” in the number of people presenting to the various clinics, which he had not definitively sought an explanation for.

“You’d hear anecdotal discussions in the mess about ‘five years’, or ‘resilience has broken down’,” he said, adding that the decline of parents’ health was also a factor.

He said there were spikes reported around the fifth-year anniversary. “But we’ve not seen anything abate that level of unwellness.”

As of the end of last month, Guardian Australia was aware of 32 federal court cases since January, including 22 brought by the National Justice Project, with 19 involving children as the primary applicant.

Some cases have also revealed an as-yet unsolved problem, with the Nauruan government seeking to block the court-ordered medical transfers by refusing permission for an air ambulance to land.

The department’s Cheryl-Anne Moy confirmed there were “some instances” where people couldn’t be moved within the ordered timeframe, sometimes because of problems with the person themselves.

Anyone with outstanding issues with the Nauruan police force cannot be taken out – and this can include those arrested for attempting suicide if police decide to lay charges – and Nauru must give approval for landings. Commercial flights have limits on the number of people with issues like mental healths issues on each flight.