when does it legally become 'my' property?

[Joe Pineapples]

Scenario is this...

A household appliance was replaced through an insurance claim, with a new one. It was agreed verbally over the phone, that they would pick the old one up, after delivery of the new item, but no firm timespan for this was mentioned. So basically i was wondering if there is a law by which the old item becomes my property, if they fail to attempt in anyway to collect it, within a certain period of time?.

(the old item is slightly faulty, but still useable, and would make a great spare )

I repaired a PC before Christmas and am still awaiting a collection. Can I do the same? There is no exchange of money because it is part of one of my jobs.