How do people store bicycles in London?
To add to Michael's comment if it's your property you can't be forbid to bring a bicycle into your apartment, unless it's somehow unlawful to be in possession of said bicycle. Would you be forbid to bring a crank set or a pair of wheels or a bar set into your apartment? Why would you be forbid to bring those things assembled in a certain way into your apartment?

Read your lease very carefully, or get a lawyer and ask him or her about your situation considering your lease. If you can meet the building owner or property manager and ask, indirectly, about bicycles, do so and get a feel for their attitude about it. If you can tell they are going to be giving you a hard time about it don't even bother, look elsewhere. Having a bad landlord and/or building owner is a whole other problem in and of itself.