London Mayoral candidates back the pedestrianisation of Oxford Street
Five candidates running for London mayor in 2016 all support the banning of vehicles from Oxford Street.
Labour Party's Sadiq Khan and the Conservative Party's Zac Goldsmith backed the idea, which could give cyclists and pedestrians more space.
But Westminster Council said businesses on Oxford Street were "not in favour of full pedestrianisation".
Stop Killing Cyclists called for 10% of Transport for London's (TfL) budget to go to cycling infrastructure by 2020.
The current 1.4% of TfL's budget being spent on cycling safety was not enough, said the group.
The Green Party's Sian Berry, the Liberal Democrats' Caroline Pidgeon and Independent candidate Rosalind Readhead all agree with Mr Goldsmith and Mr Khan's position of banning vehicles from Oxford Street.
All except for Mr Goldsmith also backed letting cyclists turn left at red lights if there are no people crossing.
Cllr Robert Davis at Westminster City Council said the governing body expected TfL to "reduce buses by 20% on Oxford Street".
He added: "We will work with the next Mayor of London, once they have been elected - but they will have to consider all the implications and engage with all relevant parties."
All candidates also supported more protected cycle lanes in the capital and fitting safety equipment to end blind spots in HGVs, the campaign said.
'Attractive and safe'
Stop Killing Cyclists co-founder Donnachadh McCarthy said the election provided an "urgent opportunity" to speed up improving London for cyclists.
He added: "We welcome the fact that all five candidates replied to our 10 by 2020 Challenge and all agree on many radical new crucial safer cycling measures."
Leon Daniels, TfL's Managing Director of Surface Transport, said it had pledged to invest £913m between 2013 and 2023 in an effort to make cycling "safer and more attractive" to cyclists.