Shadow business secretary Chuka Umunna, the Labour MP for Streatham, wrote on Twitter: "Deepest condolences to the family of the lady tragically killed at a bus stop on Streatham High Road early this morning."
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The 47-year-old man died shortly after 3pm on Tuesday.
Specialist explosive detection dogs searched through the town examining letter boxes and phone booths for signs of potential devices.
Temperatures reached 29.1C in St James's Park, central London.