A vigil will be held in Oxford tonight for the victims and their families after Wednesday's attack in Westminster.
Witney By-Election Date Set
David Cameron's successor as an MP will be chosen by voters next month.
Government Chief Whip Gavin Williamson, a parliamentary aide to Mr Cameron during his time as prime minister, moved the writ for the Witney by-election in the House of Commons.
It means voters in the Oxfordshire constituency will go to the polls on October 20.
Mr Cameron quit as an MP as he feared becoming a "distraction'' for the Government although he denied his decision was linked to Theresa May's plan to introduce a new wave of grammar schools.
His departure from Parliament came two months after he quit as prime minister following defeat in the EU referendum, at which point he insisted he was "very keen to continue'' as a backbench MP and seek re-election in 2020.
It marked a swift change in fortunes for Mr Cameron, who led the Tories to victory at the 2015 general election following five years of coalition government.
Speaking in the Commons, Mr Williamson said: "I beg to move that Mr Speaker do issue his warrant to the clerk of the crown to make a new writ for the electing of the member to serve in this present Parliament for the county constituency of Witney in the room of the right honourable David William Donald Cameron, who since his election for the said county constituency has been appointed to the office of steward and bailiff of Her Majesty's Manor of Northstead in the County of York.''
MPs agreed to the request.
They also officially confirmed the Batley and Spen by-election caused by the death of Labour MP Jo Cox will be held on October 20.
Ms Cox was killed just days before the Brexit referendum in June.
Labour do not expect the election to be ``completely uncontested'' although the Tories and Liberal Democrats are among those to say they will not take part in the poll out of respect for Ms Cox's memory.
hames Valley Police is reviewing security after yesterday's terror attack in London.
Thames Water is set to be fined for polluting the Thames with 1.4 billion litres of raw sewage.
Detectives have been questioning a man over two separate sex assaults in Reading's Prospect Park.
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