Journalist Caroline Criado-Perez has told ITV London that although she welcomes Twitter's new move to report abusive messages, there was more that needed to be done.
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"Three were standing together almost shoulder-to-shoulder in like a little wolf pack and they're staring at me...", said PC Wayne Marques.
Her nails had curled around three times before embedding in her pads.
The death toll from the Grenfell Tower fire is currently believed to be around 80 people, the vast majority of whom were from just 23 flats.