Refuge's Isobel Shirlaw has told ITV news that the domestic violence charity has "grave concerns" over Clare's Law.
Shirlaw said that, while some people may "possibly" be saved from abuse by the law, "it doesn't really do anything to address the huge problem of domestic violence in this country".
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The House of Commons Petitions Committee has said they will keep an eye on the petition and are concerned about fraudulent signatures.