Ownership of possessions left behind...

When you say they have refused to remove their property, what exactly does that mean, they never came back, the told you they were not taking it, you can't contact them, what? What was the arrangement originally that led to the storage of the items originally?

Something similar has happened to me, some contractors left a rather large and expensive piece of equipment in our home after they finished work. It was sitting there for months. I got sick of looking at it so I told them that they had two weeks to move it before it was to be disposed of. They didn't come.

In the end, I didn't actually bin it but I did send it away for long term storage in a shed in my parents place. If they ever do come looking for it, it will take a week or two before it can be retrieved.

That's an absurd suggestion. Ineffective, a waste of council time and resources and a downright lie. Hardy a Legal Discussion answer.

Pop €20 in an envelop and post to the owner telling them this is the money you got from selling their stuff that you think it is only right they have it.

When they come back crying tell them you are willing to buy it back and where can i send it too

Final warning in writing and by registered post should suffice OP, alternatively remove the items (if practical and drop them off at your former friends address and take photos. I get a sense due to the Dalling out they don't want to call to your property, but if all other efforts have failed remove the items but again, document everything.

I'm not sure if it's wise just to Dump another persons belongings.

Involving local authority utterly pointless but on returning items to your former friends property, insure its to the property and not outside on a street or pathway. I'd also consider advising Gardai if your intention is to return items to avoid any suggestion or accusations of Trespass.

Sell the property in question and the legal owner will probably turn up next week looking for it ! So what ?

The real owner might have a cause of action in the tort of conversion. Conversion occurs where the owner of property is wrongfully deprived of it's use and possession. I think that conversion might be one of those strict liability type situations i.e you held my property and now you cannot produce it so you are presumed liable.

There might be gratuitous bailment. This is where property is entrusted to a bailee [OP] with no remuneration (as distinct from a bailee for reward). Again, I think this could be a strict liability situation in that a bailee is obliged to explain why they cannot deliver up property entrusted to them.

I don't see any evidence of a contract - even implied. So, I cannot see any authority to deal with the goods in any particular way that might otherwise have been specified e.g. an agreement that goods will be disposed of within a certain time limit.

Also, I wonder if there is any risk of a theft type offence being committed if the goods are disposed of in the knowledge that such an action will permanently deprive the owner of the goods. Devil's advocate - to be caught on this hook I suspect that OP would have to have taken the goods - which they most certainly did not do as the property was entrusted to them.

Sending a registered letter notifying intention to dispose of the goods would not help IMHO as that act alone does not create a right to then proceed to dispose of the goods

Messy............

The dry cleaning or in-for-repair analogy is a good one. However, that would be grounded on an actual contract formed between customer and shop the terms being known to each party. In OP's case there is no evidence of a contract. Merely informing the lodger of the property does of itself create a right to act as if a contract was in place.