Conservative MP Amber Rudd said Margaret Thatcher would not be surprised that some people are using her death as an opportunity to protest.
Speaking to Daybreak she said: "Be very careful, because peaceful protests is ok, anything else is not."
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The 23-year-old was held on suspicion of doing an act likely to cause an explosion to injure or damage property, and endangering safety.
Three men died on the track between Brixton and Denmark Hill in south London.
This year 21 black-tailed godwits have been released into the wild after being reared in captivity as part of a project to boost breeding nu