Cuts to legal aid are forcing the closure of almost a third of Shelter's housing advice centres and compelling the Red Cross to abandon its assistance for family reunions, the organisations claim.

The decision to close down nine Shelter offices across England this month, with the loss of 80 to 100 jobs, is blamed on the withdrawal of funding for legal advice and representation for routine housing claims from 1 April this year.

The British Red Cross says the cuts will force it to withdraw expert help to those trying to bring their children into the United Kingdom to escape violence or persecution abroad and has condemned the government's economies as an assault on "family life". Citizen Advice Bureaux are also sending out redundancy notices.

The full effects of the Legal Aid, Sentencing and Punishment of Offenders Act – which slashed £320m out of the annual £2bn legal aid budget as part of the government's austerity programme – are beginning to be felt. Further reductions in the cost of criminal legal aid, by introducing competition, are now being sought by the Ministry of Justice.

According to the government's own assessment, around 600,000 people will lose access to advice and legal representation. Among areas for which it will no longer be available are: divorce, child custody, clinical negligence, welfare, employment, immigration, housing, debt, benefit and education.

Last week the president of the supreme court, Lord Neuberger, the UK's most senior judge, signalled his concern about the effect of the cuts on access to justice. He told The Guardian: "If you start cutting legal aid you start cutting people off from justice … And that's dangerous … You [may] get them taking the law into their own hands."

Shelter has been forced to shut down nine advice centres in Rotherham, Ashford, Dover, Milton Keynes, Cheshire, Gloucester, Somerset, Hertfordshire and Cumbria.

Campbell Robb, chief executive of Shelter, said: "We are going to lose about £3m a year in legal aid. Lots of benefit and welfare changes, like the bedroom tax, are coming into effect in April, just at the time that the government has cut back on legal advice. It's the perfect storm.

"We will see more people getting into the court system more quickly because we used to be able to give early, preventative advice but will no longer be able to provide that service.

"There are going to be very significant gaps where people fall through the system and won't get any representation. We will see a lot more sofa-surfing and homelessness. The scales of justice are being tipped away from ordinary people."

The Red Cross says that 90% of the refugees it currently works with require legal aid to argue their case that their children or close relatives should be able to join them in the UK.

Jonathan Ellis, head of policy at the British Red cross, said: "We are going to have to turn people away. We are not going to be able to provide the full support we have in the past.

"We have been supporting around 10,000 clients a year. I cannot believe the government really intends to do this. It is supposed to be in favour of family friendly policies."

Gillian Guy, chief executive of CAB, said: "There will be a justice gap between those who can afford to pay for legal advice and those who can't. The poorest will be unable to challenge bad decisions about benefits, unfair dismissal at work and struggle to manage any debts they might have." A number of CABs have begun issuing redundancy notices; the organisation anticipates losing £19m in annual income.

Steve Hynes, director of the Legal Action Group that campaigned against the cuts, said: "Much of the rhetoric from the government is all about high paid lawyers and very complex human rights cases but what they are cutting from legal aid is the straightforward cases that are important to ordinary people. Early advice is being taken out of the system."

Cuts to legal aid have coincided with a squeeze on local government spending, intensifying financial pressures on advice centres. Harlow Council has withdrawn funding from a local advice centre and is now facing a judicial review challenge over its decision. The council says it is funding a CAB in the town.

Most independent law centres are expected to survive: staff are being creative with their limited resources, low level charging has begun for advice in some cases and £65m – over two years – of government and lottery money has been made available to cover a "transition" period.

Other adaptations are likely. Lawyers are likely to be asked to provide more legal assistance on a free, or pro-bono, basis. At Teeside University, law students are offering free advice and some representation to the local community, while Keele University is collaborating with the judiciary, law profession and third sector to train "community legal companions" to provide assistance to litigants fighting cases on their own.

A flood of judicial review challenges are expected early in the new financial year to test the complex regulations governing what category of cases should remain in scope. While legal aid is being withdrawn for normal housing cases, for example, it will still be available for someone facing the threat of being made homeless. Legal aid has also been retained for asylum cases.

Last Friday the MoJ announced it would provide £90,000 to support the CAB office in the Royal Courts of Justice which advises litigants in person who conduct their own cases.

New powers will be in place by July enabling courts to confiscate convicted criminals cars so that they contribute towards their legal costs. Next month the MoJ will launch a consultation on introducing "price competition in the criminal legal aid market" to ensure "long-term sustainability and value for money".

Maura McGowan QC, chair of the Bar Council which represents barristers, responded by saying that: " a model based on price competition... is a blunt instrument. It assures none of the safeguards and qualities which we must expect from our justice system. It cannot be one which properly underpins the effective operation of the Rule of Law."

The justice minister Lord McNally said: "The advice sector has an important contribution to make and I recognise government has a role to play in supporting charities as they adapt to new funding realities. That's why we, with the Big Lottery Fund, are providing £65m for this over the next two years. But charities cannot escape the tough decisions councils, government departments and others have to make in the current economic climate.

"Even after the reforms come into effect, legal aid will still be running at over £1.7bn a year. Legal aid will continue to be provided to those who most need it, such as where domestic violence is involved, where life or liberty is at stake or people risk losing their home. But in cases like divorce, courts should more often be a last resort, not the first. Evidence shows that mediation is often more successful, cheaper and less acrimonious for all involved.

"I am anxious to engage all involved in our legal system in a realistic debate about how we match limited resources to the commitment of a civilised society to provide access to justice."

• This article was amended on 11 March 2013. The original said Keele University law students were offering free advice and some representation to litigants fighting cases on their own. They offer legal assistance and support access to affordable legal advice services. This has been corrected.