Theresa May is under pressure to fulfil her pledge to give people struggling with debts “breathing space” from the bailiffs as figures show that half the British population are financially vulnerable.

A cross-party group of peers, including a former Tory minister, is planning to bounce the prime minister into handing those in difficulty a grace period, during which they would be protected from enforcement proceedings and mounting interest charges. They would be able to use the time to seek help.

A proposal for a six-week “breathing space” was included in the Tory manifesto but has yet to be enacted.

With official figures suggesting that almost 8 million people are over-indebted, the government is facing a Lords rebellion over the issue. Lady Altmann, the former Tory pensions minister, has helped draw up an amendment with Labour and the Lib Dems to force the government’s hand.

A survey has found that half the UK population are financially vulnerable and that one in six would be unable to cope with a £50 increase in monthly bills. More than 4 million people are already in serious financial difficulty, falling behind with bills and credit card payments, according to a survey of personal finances by the City regulator, the Financial Conduct Authority.

Those aged between 25 and 34 are the most over-indebted. Charities are also warning that an expected rise in interest rates this week will make the situation even worse. The debt charity StepChange has said that the proportion of its clients falling behind on payments has gone over the 40% mark in the first half of 2017. More than 620,000 families in England and Wales are spending more on overdue bills than on food.

The Tory manifesto was clear, stating: “Problem debt can be hard to escape and can compound family breakdown, worklessness, stress and mental health issues. We will adopt a “breathing space” scheme, with the right safeguards to prevent abuse, so that someone in serious problem debt may apply for legal protection from further interest, charges and enforcement action for a period of up to six weeks.”

Ros Altmann, a former Tory pensions minister, is leading a revolt in the Lords. Photograph: Neil Hall/Reuters

Government insiders said there had been a battle to include the measure in the manifesto, as it was not cost-free to the Treasury. Some of the debt relates to public money such as council and other taxes. However, it was eventually included in the document in an attempt to demonstrate May’s commitment to righting social injustices.

Labour has devised an amendment to the financial guidance and claims bill, which is working its way through parliament. Lord Stevenson of Balmacara, who drew up the proposal, said: “It’s surprising that the Conservatives, having – like Labour – committed to a ‘breathing space’ scheme in their election manifesto, are now dithering on its introduction, even though they have a ready-made vehicle for doing so in the financial guidance and claims bill.”

While the Lords vote is a headache for the government, charities are pushing for the breathing space rules to be announced by Philip Hammond in next month’s budget.

Matthew Reed, chief executive of the Children’s Society, said: “A breathing space for families in problem debt is needed now more than ever. Bailiffs at the door is something that no child should have to experience, but all too many do. It can take just one unexpected cost or life event, like losing your job, to push families into problem debt.

“Falling into problem debt places enormous strain on parents and children alike: becoming ill with stress, bullied at school, or forced to cut back to the bone on food and heating. A breathing space would give these families a pause from mounting fees and being pursued by creditors while they get their finances in order and agree a plan to affordably repay what they owe. This [Lords] amendment is an important step towards giving families in debt the help they need to get back on their feet. Families simply cannot afford for there to be any delay in making this debt respite a reality, and we urge the chancellor in his autumn budget to stay true to the government’s election promise and make this happen.”

The government has said that it backs the breathing space plan, but that it needs more time to design the policy.