Well, it doesn't have to be a shed, but I need a place to store a bicycle, pressure washer, roof box and some other odds and ends. What would you suggest?
Consider the box containers that are sold in most DIY chains. They come in metal as well as plastic and would likely meet your storage needs. Most mowers now have fold down handles to take up less space. Of course nothing is 100% burglar proof. So fit whatever padlock makes you happy to the box and make sure your contents insurance covers you for outside. I doubt very much with the items you've mentioned it would come to more than a £1000 worth if it came to making a claim. Phone your insurer and talk them through it if need be and record the conversation so that if they deny the terms you've discussed later on in the event of the claim you have it on record.