I live in the same circumstances - rented terraced house with a back yard. I have two Asgard sheds for my four bikes.
They're all right security-wise but the condensation buildup is terrible in the winter. I bring the bikes in the kitchen one at a time to get properly dry, to try to prevent mould and mildew buildup. My spare tyres were all hung up in the Asgard sheds and got absolutely covered in mildew, so I need to find an alternative solution for them.
If your landlord is open to you making some kind of raised platform for your Asgard shed, even if it's just a rectangle of paving stones on top of the yard floor, that might mitigate the problems somewhat. The water running along the floor when it rains probably contributes significantly to the condensation problem. You need to check your landlord is happy for you to drill holes in their back yard as well.
Asgard fixed them to the concrete floor initially for me, and were mostly pretty good. Initially they forgot to bring the correct drill with them (yes, seriously) and said they'd come back another day to do it. A quick phone call to Asgard head office by me and that was remedied. I understand they're subcontractors so bear that in mind.
Update us on how you get on? I'd be interested to see what you decide to do. I hope you find something that works for you.
