Mayor Jules Pipe, the Chair of London Councils and Mayor of Hackney, told the London Assembly that the Government's plans to cut housing benefits have not stopped rents being increased over the last 18 months.
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A lamp in the tower which houses Big Ben is to be switched off for the first time in more than 70 years.
Sir Bruce entertained audiences for more than seven decades.
Work in the tower will also pause over the bank holiday weekend.