Government promises to improve early advice for social welfare claimants and spend an extra £6.5m are a “drop in the ocean” compared with the deep cuts imposed on legal aid spending, lawyers and justice organisations have said.

Welcoming the Ministry of Justice’s limited move to restore help in a few areas involving children, charities and professionals said austerity would continue to inflict severe damage on an already underfunded justice system.

The 290-page MoJ review fulfilled a promise to examine the impact of the Legal Aid, Sentencing and Punishment of Offenders Act (Laspo), which reduced annual legal aid expenditure by at least £350m from 2013. It acknowledged those savings may merely have shifted costs to other departments.

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The MoJ is restoring legal aid for migrant children separated from their families and those involved in guardianship cases in family courts, and will overhaul the severely criticised exceptional case funding system, which is supposed to help in cases where human rights could be breached.

An additional £5m will be made available for “innovative technologies” and testing new ways to deliver early advice face to face to those seeking help. About £1.5m will go to help unrepresented defendants who have flooded into family courts in particular, slowing down the justice system.

Advice will be improved for housing cases and possibly given by more lawyers working in GP surgeries. The financial eligibility thresholds for those seeking legal aid – which have not been raised for decades – would also be reviewed, the MoJ said.

The review contained significant admissions. It conceded Laspo was “not entirely successful at discouraging unnecessary and adversarial litigation at public expense”.

The report also said it was “impossible to say with certainty that the act targeted legal aid at those who most need it”.

Most damagingly, it said there was “limited quantitative evidence to demonstrate” money saved by cutting legal aid simply transferred costs to the NHS and other departments.

The justice minister Lucy Frazer said some of the money being provided was new and there had been talks with the Treasury. The areas where legal aid scope is being restored will also involve extra MoJ money.

“We are aiming to put forward a package to the Treasury for the next spending review armed with more evidence for our spending [on legal aid]. We will be making a bid in due course,” she said.

The report said Laspo had, overall, been “partially successful” in meeting its objectives, reducing legal aid expenditure by 20% since 2013 to £1.6bn a year.

A separate consultation on legal funding for inquests was also published on Thursday. It rejected campaigners’ calls for automatic legal representation for families in cases where police, prison officers or other state officials are given lawyers. The MoJ review said it wanted to improve advice about the existing availability of legal aid.

Christina Blacklaws, president of the Law Society which represents solicitors in England and Wales, welcomed aspects of the review: “The MoJ has accepted the case for changes in relation to the legal aid means test, exceptional case funding and early legal advice, and has committed to further work as to what those changes should look like.

“However … the government must give urgent attention to amending the means-test thresholds because the current levels are preventing families in poverty from accessing justice.”

Richard Atkins QC, chair of the Bar Council, which represents barristers, said he was disappointed. “This is a wasted opportunity,” he said. “The report offers little of substance to ease the impact of Laspo on vulnerable individuals seeking justice.”

The new cash was “but a drop in the ocean given the impact Laspo has had on restricting individuals’ access to justice”. The review provided “clear evidence that the Treasury must find a way to properly fund the justice system and reverse a decade of cuts”.

Steve Hynes, director of the Legal Action Group, said: “Legal aid and the justice system need an injection of cash. The £6-10m proposed won’t do it. You can’t replace £400m of cuts with a few well-directed schemes.”

Deborah Coles, the director of Inquest, which supports families in coroners’ courts, said: “The MoJ have failed to confront the reality of the uneven playing field faced by bereaved families, and the considered recommendations of all those who have looked at this issue. This is a dishonest response and a betrayal of those who invested in this review in the hope of securing meaningful change.”

Bob Neill MP, the Conservative chair of the Commons justice select committee, said: “There are a number of positive proposals in the review and accompanying action plan but, in several key areas, proposals for further reviews and pilot evaluations risk being seen as ‘kicking the can down the road’.”

Richard Burgon MP, the shadow justice secretary, said: “This is too little, too late. The government has wasted two years investigating the impact of its own legal aid cuts only to respond with no credible plan to end the suffering they have caused.”

David Isaac, chair of the Equality and Human Rights Commission, said: “Rights mean nothing if you cannot enforce them. Bringing back face-to-face advice will significantly help those who have faced discrimination seek justice and will be particularly beneficial for many disabled people and those with limited English language skills.”

Audrey Ludwig, director of legal services at Suffolk Law Centre, said: “The amount of money being invested is minimal and, when spread across the country, will only be enough to help those who are fortunate enough to live near a legal support hub that’s running one of the new pilots.”

Jo Edwards, of the family law organisation Resolution, said: “The £8m of funding – across all areas of the law – represents little more than 2% of the £350m of annual cuts to the legal aid budget. Nobody was expecting this review to entirely reverse the cuts, but the commitment from government to early intervention, for example, has to be backed up by meaningful funding.”