My landlady says I can't keep my bike in the house.

If it's not in the contract that you can't keep a bike on the premises I don't think you have an issue. She may of course decide not to renew your lease but you won't be in breach of contract so you're fine until then.

My contract says I am not allowed to keep pedal cycles in the flat but I had five at last count.

Who are these people who write these things? WTF is a pedal cycle? I know what they are attempting to refer to but FFS.

@Sharkstar, did you just remove your pedals on your your 5 bikes for each rent inspection to get around the wording in your contract?