Conservative Lambeth Councillor Julia Memery told Liz Wickham that it's a civil case and they expect an eviction by Monday at the latest, if the travellers have not moved on voluntarily by then.
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In a wide-ranging Peston on Sunday interview, he said Parliament security needs reviewing and the PM's counter-terror strategy is flawed.
The terror attack carried out by Khalid Masood at Westminster that left four people dead lasted less than two minutes say police.
Two knives were found at the scene in Islington, North London, and the suspects fled on foot before being arrested.