Why don't you hire a bike from a bike hire shop, mention that it's for charity and strike up a deal with advertising so you can get it gratis?
@Wicksie started
London Fixed Gear and Single-Speed is a community of predominantly fixed gear and single-speed cyclists in and around London, UK.
This site is supported almost exclusively by donations. Please consider donating a small amount regularly.
Why don't you hire a bike from a bike hire shop, mention that it's for charity and strike up a deal with advertising so you can get it gratis?