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 study by the National Childbirth Trust and National Federation of Women's Institutes found a lack of staff left some women frightened.
Extracts released by 10 Downing Street suggest Mrs May will say the UK will not settle for a "half-in, half-out" policy.
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