The forensic investigation is still ongoing at the home of Oscar Pistorius following this morning's shooting, a spokeswoman for South African police has said.
She said the police would not confirm the identity of the shooting victim until her family formally identify her.
She confirmed there are no other suspects involved in the death.
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The chancellor now faces the prospect of forming a minority government or calling for a snap election.
The 73-year-old said a return is unlikely "given the politicised atmosphere that seems to have afflicted our set."
Chancellor Philip Hammond said the UK will make a financial proposal to the EU in the next three-and-a-half weeks.