The cut, which would mean a loss of about pounds 20 a week in income support, is among steps being proposed by the Government to persuade mothers to co-operate with the CSA.
Other proposals include unannounced check visits at claimants' homes and faster investigations of CSA suspicions.
At present, lone parents who fail to co-operate with the CSA risk losing 20 per cent of their pounds 49.70 income support for six months, and 10 per cent for a further 12 months. Now the Government, which is considering Australia's system of making benefit conditional on co-operation, wants to increase that.
Such plans will enrage pressure groups which say the Government has failed to understand why many women do not co-operate with CSA attempts to track down fathers' money.
They say it is not because they are in collusion with ex-partners but because they are often frightened of them and want no contact. A woman in Birmingham, for instance, is not co-operating because her ex-partner is now a convicted sex offender and she does not want him to have access to their child.
Details of the penalty plan are due to be given to the House of Commons social security select committee's hearing on the workings of the CSA on Wednesday.
Written evidence from junior Social Security minister Andrew Mitchell says: "It is clear ... that the existing reduced benefit provisions are failing to provide sufficient incentive to co-operate with the child support provision.
"We are considering whether to increase the amount, say to 40 per cent of the personal allowance. Obviously this would apply to those who did not make any contact at all with the CSA but it might be applied more
It continues: "We have also asked the Benefit Agency to consider what further measures can be taken to prevent lone parents from receiving benefits to which they are not entitled. Possible steps include unannounced check visits to claimants at home before benefit is awarded."
Sally Witcher, director of the Child Poverty Action Group, said: "Parents should not be ... compelled to choose between pursuing maintenance against their better judgement or seeing their children experience hardship."