Section 2, Theft Act, 1968:
"A person’s appropriation of property belonging to another is not to be regarded as dishonest . . . if he appropriates the property in the belief that he would have the other’s consent if the other knew of the appropriation and the circumstances of it;
or . . . if he appropriates the property in the belief that the person to whom the property belongs cannot be discovered by taking reasonable steps".
If, for example, you take something out of a skip in the belief that the owner has dumped the item and won't mind if you take it, you're not committing any offence. (It's irrelevant as to whether the owner would actually give his consent. As long as you believe that he would do so, it's legal).
Similarly, if you see a pound coin on the pavement (and you can see no way that its owner could be traced) you can lawfully pick it up and keep it.
The situation you describe seems to be analogous to those I've mentioned, so it's lawful to clear the bike shed. (The only exception would be if someone stated that something in the shed was their property and that they didn't want it disposed of. You couldn't then simply 'junk' the item but you could still take it out of the bike shed and leave it on their doorstep).
Chris