David Cameron has said he will look "very closely" into the case of Riven Vincent, the mother who announced online that she was considering putting her daughter into care because she no longer felt able to cope.

The prime minister's intervention came as Vincent received online support from other parents of disabled children.

Dozens posted messages detailing the difficulties they have getting social services' support, and charities stressed that Vincent's case was not unique, warning that the problems facing families could get worse because of local authority budget cuts.

The prime minister denied the coalition's austerity measures were preventing the family getting more help.

Cameron, whose son Ivan had cerebral palsy and severe epilepsy and died in 2009 aged six, said: "I have every sympathy with the incredible difficulty that families have with bringing up disabled children.

"I know how tough and hard it can be, and how so many families can get to the end of their tether and just not know how they are going to go on caring for someone they absolutely love and feel a great joy from, as well as a huge amount of challenge in their lives.

"Obviously, I'm going to look into this case very closely and have already started to do that."

Cameron visited Vincent before the last election to assure her that if he became prime minister he would not do anything that would harm disabled children. She said today that she had hoped "he would have done more to protect families like ours".

Vincent put out a statement this morning reiterating that her family was unable to cope. "We are crumbling," she wrote. She stressed that she was anxious for her own daughter's future but was very conscious that her position was one shared by many families across the country.

"I have no wish to put my daughter into a home. We want to look after her, all I am asking for is a little more support. Without this we simply cannot cope and nor can families up and down the country just like ours," she wrote.

Vincent cares full-time for her six-year-old daughter, Celyn, who has severe quadriplegic cerebral palsy and epilepsy. As her daughter grew older, caring responsibilities became more arduous, so Vincent turned to social services hoping for extra support. When she contacted social services originally to request that her weekly allocation of six hours' respite care be increased, she was told that there "was no budget for it".

On the Mumsnet website, where Vincent posted her desperate decision to hand her daughter over to a care home, other parents described their worries about changes to the support arrangements for families with disabled children.

One mother with three disabled children said she was concerned that each of her children would lose out once the Labour-initiated Aiming High for Disabled Children programme comes to an end at the beginning of April.

"My boys were given a 'buddy' each under the Aiming High scheme. This gives our family much-needed respite for a few hours each week. It started this week but will be gone by March because the Aiming High money wasn't ringfenced and they lost it," she wrote. "We are terrified of what they are going to take away next."

Richard Hawkes, the chief executive of the disability charity Scope, said: "Families with disabled children are already heavily reliant on public services for access to social care support and with local authorities facing budget cuts of 28% it's likely we'll see more of these budgets being squeezed. Whilst the government has committed £800m for respite, this money hasn't been ringfenced so essentially local authorities can spend this money where they choose.

"We think the government doesn't fully understand the pressures and the realities of disabled people's lives or they wouldn't be making decisions that have such a detrimental impact on these families."

Clare Gent, strategic manager with the charity Action for Children, which is contracted by local authorities to provide short breaks and extra care for families, said there was great uncertainty about whether councils would extend their contracts after March, when the Aiming High money comes to an end. "Some local authorities have extended our contracts by three months, while they work out how much money they have, but it's a very patchy picture."

The £800m promised by the government is for short breaks for carers of disabled children over the next four years. "The only thing that makes that fragile is that it is not ringfenced. There is nothing that requires councils to spend that money on short breaks. We think there will be competing demands on that money."

A lot of progress had been made in the provision of support for carers of disabled children under the Aiming High programme, she said. "My big fear would be that, without ringfencing, the progress made is undone, and we revert to a patchwork of service provision."