From April, working parents will only be able to claim a maximum of 70 per cent of their childcare costs, down from 80 per cent under the current system.
A survey of 2,000 working mothers carried out by the Resolution Foundation in partnership with Netmums also found that nearly 80 per cent of respondents were unaware of the change.
One in five mothers (22 per cent) said they would have to give up work because of the increase in the cost of their childcare and 29 per cent said they would reduce their working hours to cope with childcare costs.
More than a quarter said that they would have to rely on informal childcare from family and friends to make up for the loss in tax credit.
Of those respondents who said they would stop working altogether, 65 per cent used nurseries, while only 15 per cent relied on family and friends for childcare.
Mothers were more likely to say they would reduce their hours if they were in full-time employment, while part-time workers were more likely to consider leaving work altogether (see table).
Previous analysis by the Resolution Foundation of changes to tax credits showed that families earning under £30,000 annually stand to lose an average of £440 a year, with some losing as much as £1,300.
Around 470,000 receive the childcare element of WTC. The Government has said that the reduction in support will save the Government £270m next year.
Gavin Kelly, chief executive of the Foundation, said the research clearly showed that cuts to tax credits would not 'give the Government the savings they claim because a significant proportion of parents will be forced to reduce their working hours or even give up work altogether.'
Sally Russell, co-founder of Netmums, said, 'Many mothers with young children struggle to find work that pays enough, and removing childcare support for those on the lowest income will force many out of work.'