Making eligibility for legal aid in divorce and custody cases dependent on accusations of domestic violence will create a "perverse incentive" that encourages false allegations, according to a group of MPs.

Ministers should reconsider plans to restrict financial support in family courtroom disputes to only those where physical abuse is a feature, the justice select committee said.

There is political consensus over the need to cut the UK's annual £2.2bn legal aid bill because it is "one of the most expensive in the world", a report by the group said. But some of the solutions being pursued by the Ministry of Justice risk being counter-productive, it cautioned.

Poorer and more vulnerable groups could be hit hardest by the reduction in support and there is danger that such reforms could lead to inflated costs in other areas of the legal system, the committee suggested.

In a sideswipe at the Department of Work and Pensions (DWP), the study expressed concern at "poor decision making" on social security payments, which had led to a doubling of appeals over disputed benefits that received legal aid or help – rising from 72,000 cases in 2004/5 to 144,000 in 2009/10.

A punitive mechanism could be introduced to force the department to pay for legal costs when it is in error, the report said. "There is potential for such a 'polluter pays' principle to be extended considerably, with the DWP ... required to pay a surcharge in relation to the number of cases in which their decision making is shown to have been at fault.

"Rejecting this idea as a 'robbing Peter to pay Paul' transfer of funds around the public purse, the minister is overlooking the potential benefit such a policy would have in providing a financial incentive to public authorities to get their decisions right first time."

The Ministry of Justice's aim is to trim £350m from the annual legal aid budget. Most of the savings will come by reducing the types of cases entitled to public funding.

Controversy has centred on family law, where most claimants will no longer be able to apply for legal aid unless domestic violence is an issue.

"We are concerned that using the presence of domestic violence as a proxy for the most important cases will lead to a perverse incentive to make false allegations of such violence," the select committee warned.

It will also ensure that domestic violence, where it has occurred, will feature more prominently than it might otherwise have done, harming children and adding unnecessary expenses, it added.

If the government was to insist on using domestic abuse as a criterion for eligibility, it should ensure that the definition "incorporates non-physical abuse", the report said.

In terms of restricting access to justice, the reforms could lead to an influx in poorly informed litigants clogging up the courts. "The ability of the most vulnerable people to present their cases will be weakened because they will not have had help and advice in preparing them," the report said. "This could deny justice to the individuals concerned and increase the time and expense necessary to deal with cases at tribunal."

The precise impact of the changes could not be predicted, the MPs continued, and they would impose a severe strain on the voluntary sector, straining David Cameron's vision of a "big society". The report said: "Organisations in this field have made it clear they do not believe it will be possible to meet all the demand which will be created by the proposed changes to legal aid."

The chairman of the justice select committee, Sir Alan Beith MP, said: "There is a cross-party consensus on the need to reduce the cost of the legal aid budget, which is one of the most expensive in the world.

"Concerns remain, however, that there is the potential for vulnerable groups of people to be disproportionately hit by the changes. The government's proposals need considerable further refinement before moving forward and alternative ways of achieving savings should be examined."