WENDY Morrison, 51, of Aspley, and Susan Henderson, 37, of Canning Circus, will both be stung by the new "bedroom tax" from April.
Ms Morrison, who lives with her 12-year-old daughter in a three-bedroom house in Bells Lane, said the £40 loss in housing benefit a month would have a big impact.
Working 16 hours a week in a bar, she said: "My daughter will lose her pocket money. It will kill us. I was told to take in a lodger. No man comes in my house, no strange woman comes in my house.
"But if I don't pay the £10 extra a week, we'll be evicted."
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Ms Morrison, who has lived in the house for 13 years, added: "Why should I have to move out of a community that I've been in for that long?
"It makes me feel sick. I'd have to bid again [for a new house] but I've been told it would take two years because there's not enough two bedroom houses."
Ms Henderson, who lives in a three-bed house in Portland Road, Canning Circus, faces the prospect of moving her two sons, aged five and nine, into one room in a new two-bed house. The Government says children of the same sex under 16 must share a room. But Ms Morrison, who believes her oldest son might have autism, said: "He needs his own space, he loves his own space."