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

"There are also secure bicycle racks and/or sheds."

i would argue that this reads as there are secure bike racks/secure sheds.

if when you get there check if this is the case and if the shed isnt secure then keep your bike in your room till they make it secure. clearly secure is a subjective thing but im sure you could easily get the police round for a security check and they could provide a written thing saying the shed is not secure unless they put in fat ground anchors etc. if their secure areas arnt secure enough to pass an insurasnce inspection they arent secure. so tell them you'll keep it in the house till there are massive anchors to lock to. or something.*

*having no experience of this i have no idea if this is bolocks or not.