Plans to award legal aid contracts to the lowest bidders following criticisms it would reduce justice to a "factory mentality" have been scrapped.

The justice secretary, Chris Grayling, ditched the proposals after drawing up the government's latest legal aid reforms with the support of the Law Society, he told the Times.

Barrister-turned-MP Karl Turner had earlier raised fears that price-competitive tendering for legal aid would allow multinational firms to provide justice at the cheapest cost.

The Labour MP had told MPs he believed it would lead to private companies such as G4S and Serco dominating the legal aid market at the expense of smaller firms that possess greater expertise.

Intensive talks have continued throughout the summer between the Law Society, which represents solicitors in England and Wales, and Ministry of Justice officials in an attempt to render the changes more acceptable to the legal profession. Grayling has been closely involved.

The MoJ is expected to launch a fresh consultation on a redesigned set of measures. The same savings of £220m are still being sought, through cuts to fees and other measures such as cutting back on some pre-trial hearings that could be carried out by email or videolink instead.

The Times reported that Grayling will confirm the removal of legal aid in 11,000 cases brought by prisoners each year and an end to automatic legal aid for defendants with a combined annual disposable income of £37,500 a year and at least £3,000 in the bank each month after essential bills.

The Law Society confirmed there had been intensive talks with the MoJ over the past six-and-a-half weeks. "The Law Society has not had a summer holiday," an official said. "We have had meetings on a weekly basis all through the break."

Another proposal that has attracted widespread criticism is the structure of fees, which it is claimed will lead to more defendants being encouraged to enter early guilty pleas. "It will be a financial incentive for the defendant to plead guilty," Turner, who initiated the debate, told MPs on Wednesday.

Steve Hynes, the director of the Legal Action Group, said on Wednesday: "If the government backs down on competitive tendering, that's a victory for the Law Society, but I would be extremely surprised if they back down on the volume of fee cuts.

"They will keep the existing number of suppliers in the system at a time when there's a decreasing volume of work. You will get the same number of providers scrambling for a lower volume of cases.

"The government will still save its £220m while some law firms will go to the wall because they won't have sufficient work. Fee cuts of up to 30% in high-costs cases means the government has barristers squarely in its sights."

The dropping of price-competitive tendering is the MoJ's second climbdown over changes to legal aid. It has already abandoned proposals that would have prevented defendants from choosing which solicitor represents them.

Defending the need for savings, the MoJ said: "At around £2bn a year we have one of the most expensive legal aid systems in the world. At a time when everyone is having to tighten their belts we cannot close our eyes to the fact legal aid is costing too much and has mushroomed into something far bigger than it was intended to be.

"We are clear we must protect everyone's right to a fair trial, and our proposals would do just that. Lawyers would still be available to anyone needing advice or charged with a crime, just as they are now. The justice secretary has been very clear this is a genuine consultation and that he expects a short period of further consultation on certain changes, for example how to add client choice. This is expected to be published imminently."

Sadiq Khan, the shadow justice secretary, said on Wednesday: "Although I welcome reports the Tory-led government is about to abandon parts of its half-baked plans for criminal legal aid, I fear mark two will still deny access to justice to millions whilst reducing our justice system to a two-tier one with only the wealthy being able to secure a fair trial.

"Chris Grayling needs to go much further and listen properly to experts and campaigners. Instead he has pushed ahead regardless with his botched proposals. I fear these plans are still unworkable and would lead to miscarriages of justice.

"We will study in detail the new consultation the government is expected to launch tomorrow."