The BBC poll, taken in the light of the Tour de France which starts in Leeds this weekend, also reveals that only a third of respondents believe that roads in the local area were designed to be safe for cylists.
This is despite the fact London Mayor Boris Johnson is promising "unprecedented" investment in the Capital's roads and cycling networks.
Mr Johnson said: "This funding, together with the investment through my roads and cycling plans, means the improvements being delivered in partnership with London’s boroughs is simply unprecedented. Safer cycling routes and better open spaces not only make our city safer but they also boost local economies encouraging people to support their local high streets."
The Department for Transport (DfT) has also said it had doubled funding for cycling to £374m to help deliver safer junctions.
However, Chris Boardman, Olympic medallist and British Cycling policy adviser, told the BBC: "It's clear...people don't feel safe when riding their bikes on our roads.
"In order to rectify this we need a clear commitment from government and local authorities to prioritise the safety and needs of cyclists in all future transport schemes."