Louise Ryan, 41, who lives with her husband and two children in Islington, north London, will see the £438-a-week benefit, which covers the rent, reduced to £340 under the changes to housing benefit introduced this month.

"With the cap, we would have to find £98 a week out of our benefits when the changes come in," she said. "I understand that in some places £340 would be ample, but not in most places in London – and it's not like we're living in some kind of luxury apartment."

Ryan says that it's the impact on her children and their education she fears most. "If it was just the two of us, then it's not so much of an issue; but when you've got kids, you can't just move to a studio flat. I don't really want to have to move the children from their school either, because they're doing well."

The family's uncertainty about the future has been heightened after they found they couldn't move house without giving their landlord two months' notice. Most alternative accommodation they can get is only available at short notice, and the couple can't afford to pay overlapping rents.

Ryan said: "If we give the landlord two months' notice then we are putting ourselves in a position of homelessness if nowhere is available at exactly the right time. That's the worst case scenario. Charities such as Family Action have warned that the government's changes, including a cap on the amount a claimant can receive, will leave poor families with a stark choice: to rack up debts, move into temporary accommodation, or become homeless.

Karen Browne, 52, has been preparing to move out of her home in Halifax, where she has lived with her disabled husband for six years – because she has too much space. She said: "We're having to downsize at our own expense because of all this. It's going to cost us to move simply because of this. Even though we've spent a lot of money on this house, we're going to have to leave it all behind." At present, benefits cover the £95-a-week rent, but the couple say they are facing a 25% cut to their housing benefit because they have three bedrooms.

She said: "If we lived in a one-bedroom property, it would be horrific. We need a spare room for a carer and when my husband's health is bad he needs to be in a room on his own."

The issue of having too much space has cost the coalition a key vote in the House of Lords. Peers voted in December to block the government's attempts to classify "over-occupiers" as people who have more than one spare bedroom – and instead made clear this would only apply to those with two extra rooms.

However, until the welfare bill passes through the upper house, claimants and councils are unclear about what will happen. The complexity of the benefits system has also meant months of uncertainty ahead for Browne.

She says it is still unclear whether her 31-year-old son, who lives on his own and has mental health problems, will have his benefit cuts because he also has a spare room which is used by overnight carers. "[The council] haven't said whether he'll have to downsize or not, they've not given us enough information. We don't know if he'll be exempt because of his disabilities. If they cut his benefits and he doesn't move, he'll end up with loads of debt."

Cuts to housing benefits have triggered a race for smaller houses, and those who can't get suitable properties in time could be forced into debt if they can't make up the difference in rent payments after benefit cuts are introduced.

Browne said: "There are very few properties available in this area and they're not building any more. Everyone's after them now, because of this – people are queuing up for them. It's a case of bidding and crossing your fingers. What are we meant to do in the meantime until we get a property that's suitable?"

She added: "We're stuck in this position. Whoever is making these decisions has obviously never been in the position of being poor."