The Women’s Institute and Mumsnet are among a powerful alliance of women’s groups that has written a private letter to justice secretary Kenneth Clarke, warning that the government’s plans to reform legal aid will hurt victims of domestic violence.

A letter copied to the prime minister, David Cameron, signed by the two organisations, along with Netmums and Rights of Women, expresses fears that the reforms will deny legal aid to tens of thousands of women who are trying to leave abusive partners.

The alliance’s criticisms threaten further headaches for the government and the Tories in particular. The party has been desperately trying to woo women voters, and claims that its legal aid reforms will penalise domestic violence victims could become a high-profile cause for its critics. It is understood that Number 10 is increasingly nervous about the issue and has sought meetings with the Ministry of Justice over the bill’s progress.

Last week, the government presented amendments to its Legal Aid, Sentencing and Punishment of Offenders Bill as confirmation that it was safeguarding legal aid for domestic violence victims.

Clarke said that “the government has responded because of our concern on domestic violence pretty generously”, and suggested the amendments were “fairly formidable”.

But women’s groups are furious that what the government has presented as a U-turn applies only to women who enter a refuge, and not to those who access domestic violence support services in the community – for instance, through specialist charities.

In its letter to Clarke, obtained by the Observer, the alliance points out that “the vast majority of women who experience domestic violence do not go into refuges”.

In 2010, the latest figures available, 124,895 women accessed services from Women’s Aid, the charity helping domestic violence victims.

Only 17,615 of these were admitted into a refuge. Women’s Aid’s annual survey revealed that, on a single day in 2011, 224 women were turned away from its refuge services, mainly because of a lack of beds.

In its letter the alliance explains that many women do not report violence to the police or other authorities.

It claims: “We know from our work with victims of violence that women most often seek shelter and comfort from family and friends after experiencing violence; a natural and understandable reaction to a traumatic situation.

“Other women who do not have this option may try to access refuge support, but are turned away because there are no bed spaces.”

The alliance is calling for the government to introduce a series of amendments when the bill returns to the Commons, to establish broader criteria for determining which domestic violence victims are entitled to access legal aid.

Its letter concludes: “We feel strongly that women should be encouraged to take whatever route out of domestic violence they feel comfortable with, and should not be denied access to vital legal support because they have chosen not to report the violence they have experienced to statutory agencies.”

A spokesman for Sound Off for Justice, the group that campaigns against the Legal Aid, Sentencing and Punishment of Offenders Bill, echoed calls for the government to think again on domestic violence aspects of the proposed legislation.

“This is a crime that affects the lives of women, men and families,” the spokesman said.

“For over a year, we have warned the impact of this cut will not be to save money but to leave thousands of victims with no way of escape. The government knows this is an attack on the family and on women.”