Sir Hugh Orde, President of the Association of Chief Police Officers, said British police do not "want to be armed" and "guns do not necessarily solve the problem", during an interview with BBC Radio 4.
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Marjorie and Michael Cawdery, both 83, are understood to have been stabbed to death in a killing their family called "incomprehensible".
Detectives have launched a murder investigation following the shooting in Brent, north west London on Friday night.
Hot and humid throughout the Bank Holiday Weekend.