Lord Tebbit, the former Conservative minister campaigning to preserve legal aid for children in medical negligence cases, has revealed that he enjoys being "on the side of the angels for once" in opposing cutbacks.

Explaining why he supports amendments challenging government legislation aimed at saving £350m a year, the one-time MP for Chingford said he feared that some of the economies proposed by the Ministry of Justice may be "going too far". His comments came as the House of Lords began its critical examination of the legal aid, sentencing and punishment of offenders bill which removes legal support from those pursuing cases involving medical negligence, debt, housing, welfare and family disputes.

Long vilified for his self-help approach to reducing unemployment, after he urged the jobless to get on their bikes to find work during the 1980s, Tebbit has recently voiced concerns about government plans to reform the NHS.

He has now put his name down – alongside that of Lord Newton, Margaret Thatcher's last social security minister – to two, linked amendments that would ensure children, or parents on their behalf, will be entitled to legal aid if they need to pursue medical negligence claims.

"I'm inclined to support those amendments," he told The Guardian. "I think [they] ought to be debated at length. There are cases where there should be legal aid for children in medical negligence cases."

Tebbit, whose wife was left paralysed in the IRA's bombing of Brighton's Grand hotel in 1984, said he backed the "broad thrust" of the government's bill which is aimed at saving money.

"I'm not in the business of making rich lawyers richer," he said. But in relation to depriving claimants under the age of 18 from having access to legal aid for medical negligence claims, he said: "In that area [the bill] may be going too far. I want to hear all the arguments. It's right that it should be debated."

Asked whether he had discussed his misgivings with the justice secretary, Ken Clarke, he replied: "I find that cabinet ministers, with one or two exceptions, don't speak to me."

"I haven't asked to go and see [Clarke]," he added. "I'm not sure that my advocating such a concern would be the best way of making progress with it."

Tebbit had taken up the cause, he said, because: "I have listened and read the arguments … and I think there's sufficient in it that we ought to [examine]. It's nice to be on the side of the angels for once."

No votes are expected in the Lords on the legal aid bill until next year. Most peers speaking on Tuesday opposed the government's plans.

The first amendment debated requires the government to "secure (within the resources made available…) that individuals have access to legal services that effectively meet their needs".

Lord Goldsmith, the former Labour attorney general, said it was "a way of testing whether this government will sign up to the principle that there's an obligation on them to secure justice for those who need it".

Lord McNally, the Liberal Democrat justice minister, replied that Labour, if it had won the last election, would have had to make deep cuts to legal aid expenditure.

Earlier, before the debate, Labour peers opposed to the bill held a mock funeral outside parliament standing beside a coffin alongside signs declaring "RIP legal aid".