Victims of domestic violence will be given greater access to legal aid to fund civil cases against abusive partners, Kenneth Clarke announced on Tuesday as the government made a U-turn on some of its controversial reforms. The justice secretary described the amendments to the legal aid, sentencing and punishment of offenders bill as "fairly formidable".

As MPs debated the bill after peers inflicted 11 defeats on the measure, Clarke attempted to reach out to opponents by relaxing the rules for proof of domestic violence.

Under the government's original plans, a victim of domestic violence – male or female – would be able to apply for legal aid for civil proceedings, such as divorce, only if they pursued their case through official legal channels. Legal aid is available in all cases for restraining orders.

Clarke announced that the government would extend the definition of domestic violence to cover evidence from a refuge for victims and evidence from a GP. The government will also extend from one to two years the time period in which a victim of domestic violence can claim legal aid.

Clarke said: "The government has responded because of our concern on domestic violence pretty generously."

One ministry of justice source said: "What we are doing is, in practical terms, identical to what those calling for concessions have requested. There will be a blanket exception for people who have been victims of domestic violence over the last two years."

Clarke announced that he would not accept a Labour demand to grant legal aid to all child medical negligence cases. The justice secretary said there was no need to back down here because lawyers offer to take on such cases on a no-win-no-fee basis.

But he said that legal aid would be available for cases involving brain-damaged babies. This is because lawyers are unwilling to take on such cases on a no-win-no-fee basis because of the high costs of medical reports that need to be carried out in the early stages of a legal case.

The justice secretary said he would not be making any further concessions. "We have moved in key areas beyond where we were and this evening we have to insist that is where we will end," he said.

"There comes a point where we will forget what the object of this is. We do want more of these cases not to be conducted by lawyers financed by the taxpayer engaging in adversarial litigation about where children are going to live, what maintenance should be paid by one party or the other, or what share of the matrimonial home is going to be owned by one party or the other."

The legal aid, sentencing and punishment of offenders bill (LASPO) suffered 11 defeats in the House of Lords — far more than the controversial NHS reform bill that was recently signed into law — reversing many of the savings promised by the Ministry of Justice.

The MoJ has pledged to overturn all but three of the defeats in its determination to save around £350m a year from the department's annual civil legal aid budget. It has agreed to accept that the new director of legal aid casework should be independent, that legal aid should be preserved for appeals to the upper tribunal, court of appeal or supreme court in welfare benefits cases, and to amend the bill's definition of domestic violence.

In a sign of division within the coalition, several Liberal Democrats, led by the party president, Tim Farron, tabled an amendment to extend legal aid to lower tribunals for benefit cases, although they did not ultimately push the amendment to a vote.

Clarke said he was prepared to examine an extension to the lower level. "I can conceive of cases in the lower tribunals where there might be cases where it is a point of law. Is there some situation where someone, preferably the tribunal judge, certifies there is a point of law involved where legal aid should be available?

"We haven't got that at the moment. But just as we've accepted the argument about these legal issues in the upper-level tribunals, of course, if the same thing arises in the lower tribunals, we could do so. We will go away and work on it with the Department of Work and Pensions to see if some equivalent where it is certified by someone other than the claimant themselves or the claimants lawyer, that there is a point of law. We have retained for ourselves powers to amend these things by regulation, so we could solve the problem and bring something forward by statutory instrument."

In advance of the vote, Sadiq Khan MP, Labour's shadow justice secretary, said: "The bill was chopped and changed at the last minute, with insufficient time given to debate critical sentencing proposals that affect public safety.

"The government has faced fierce opposition to their slashing of legal aid, which will result in thousands of the most vulnerable in society being blocked from exercising their legal rights."

After the Liberal Democrats failed to table their amendment, he added: "Liberal Democrat MPs had the opportunity today to support Labour's attempts to protect legal aid for those on the end of flawed benefit decisions.

"Alas, they spectacularly failed, and should squarely share the blame with their Conservative colleagues for the impact this decision will have on the many thousands of vulnerable people denied access to justice."

Legal organisations and welfare charities have united in opposition to the reforms, which they claim will not save the sums the government claims.

Michael Todd QC, chairman of the Bar Council, which represents all barristers, said: "During the report stage and third reading of the LASPO bill in the House of Lords, the government was defeated on a staggering 11 amendments, in some cases by a large number of votes.

"Peers from all three main parties, Plaid Cymru and crossbenchers were moved to speak against this damaging piece of legislation.

"All the amendments aim to ensure that the most vulnerable in society continue to receive the support they need to resolve their legal problems. Many will cost very little in practice, whilst others will generate substantial savings further down the line, as problems are resolved at an earlier opportunity, thus relieving the taxpayer of greater expenditure at a later stage."

With the exception of the concessions granted by Clarke, the government ultimately succeeded in overturning all the amendments put forward by peers. The bill will now return to the House of Lords, raising the prospect of "ping pong" in which the bill shuttles between parliament's two houses.