Michael Adebolajo, 29, has been given a whole-life jail term at the Old Bailey for the murder of soldier Lee Rigby.
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The 76-year-old will continue to host BBC Two quiz show Mastermind.
Mr Rees-Mogg also maintained the Queen was ‘in no way misled’ over the decision to suspend Parliament.
The court will hear from parties including former prime minister Sir John Major and the Welsh and Scottish governments.