Criminal courts across England and Wales will be severely disrupted next month when barristers and solicitors escalate their protests against legal aid cuts by staging a full-day walkout.

The increasingly bitter dispute is threatening to undermine the ambitions of the justice secretary, Chris Grayling, to stage an international conference on the 800th anniversary of Magna Carta next year celebrating the achievements of the British legal system.

Last month lawyers staged a half-day boycott of hearings at magistrates and crown courts for the first time ever to highlight opposition to the Ministry of Justice's proposals for slicing £220m out of the annual legal aid budget.

The next protest, planned for Friday 7 March, will last all day and involve barristers abandoning their own cases and refusing to cover for what are known as "returns" – cases dropped by other members of their chambers. It is likely to lead to far more hearings being cancelled; there will also be demonstrations.

The decision to go ahead with a second walkout follows an unproductive meeting between criminal solicitors and Grayling at the Law Society on Tuesday. Under MoJ plans, some fees will be cut by up to 30%.

There is mounting resentment among lawyers who rely on legal aid payments for both prosecuting and defending criminal cases. They say successive reductions in fees since 1997 amount to cuts of 40% of their income.

Nicola Hill, president of the London Criminal Courts Solicitors' Association (LCCSA), said: "The Ministry of Justice just isn't listening. We have shown that the these cuts aren't necessary and the savings will happen naturally from falling crime and improving efficiencies in the courts.

"But the government shows no sign of hearing that evidence. Under the proposed rates, solicitors will be paid so little they won't be able to prepare cases to the required standards, leaving their clients, whose liberty, families and livelihoods are at stake, with second- and third-rate representation.

"It's ironic that almost 800 years after Magna Carta was signed, the MoJ seems set on destroying a criminal justice system that is revered around the world." Limiting the number of duty slots for solicitors paid to attend suspects in police stations would "slowly strangle" many legal firms and force them to close, she warned.

Nigel Lithman QC, chairman of the Criminal Bar Association (CBA), said: "[The government] do not care about the impact on the future of the criminal justice system in this country. They do not care about the fundamental rights of the thousands of individuals who may need access to justice, fair and proper legal representation in the future.

"They are not at all bothered about the long-term risks to public safety – especially when there is a lack of expert and experienced professionals to undertake complex prosecutions in years to come. They do not heed the risk they run of losing the billions of pounds of investment that the legal services industry currently attracts to the UK. The independent criminal bar cannot survive such cuts and the fabric of the criminal justice system will be ripped apart as a result."

At a meeting last weekend, criminal barristers and solicitors raised the possibility of shaming the justice secretary into reconsidering the cuts by withdrawing support for a high-profile Magna Carta anniversary conference that Grayling is planning early next year.

In a further sign of austerity within the justice system, the supreme court has this week issued a guide to those who are forced to represent themselves in court because of the withdrawal of legal aid for many types of claims.

The court said it had seen a rise in the number of litigants in person making applications for permission to appeal over the past three years from 13 cases in 2011 to 17 in 2012 and 22 last year. Because of the court's high profile, in most cases lawyers had volunteered to act pro-bono, unpaid, where permission to appeal was granted. In one case, a litigant appeared unrepresented by a lawyer before the justices in the UK's highest court.

A supreme court spokesman said: "While the number of parties seeking permission to appeal to the supreme court without legal representation is relatively small, we do anticipate the proportion will grow as changes continue to be made to legal aid funding throughout the UK. The new guide is designed to help answer the most common questions asked by those who approach the supreme court to appeal [against] a decision, rather than to serve as a comprehensive guide to court procedures or advocacy skills.

"The most common issue is that those without experience of the legal system require assistance in identifying whether or not an appeal can even be considered by the supreme court. We are grateful that, up until now, we have benefited from the generosity of lawyers acting for no fee, if a case proceeds to a full hearing."

An MoJ spokesperson said: "At around £2bn a year we have one of the most expensive legal aid systems in the world, and it would remain very generous even after reform. We do not underestimate the challenge this reform presents for lawyers, but there continues to be severe financial pressure, being felt by all, and we cannot avoid making difficult decisions to help resolve this. We are examining every area of the department's work to find savings – legal aid has not been singled out.

"We have not stopped talking to barristers and solicitors since we first started consulting on these reforms and have made many adjustments to our proposals as a result. We have not yet published our final plans and remain committed to sensible discussions with lawyers where that is possible. Those working within the criminal justice system will of course do everything they can to minimise the upset this disruption could cause victims and witnesses."