Its looking like a scam. The police are going to be contacted soon, some guy showed up at our house this morning at stupid o'clock claiming to be from City Link. My mum was more bothered about getting to work safely than messing about with this phone so just gave the package to him but she has said he was very convincing. :/
All that was on the letter with the phone was our full address and name/item number for the phone.
You just got scammed.
The "city link" guy is a scammer who has signed up your dad for a contract using his stolen details, probably online and used any old debit card ( not yours however just another one he has nicked ) to make up some bank details. The phone gets delivered to you ( and signed for... this is the very bad bit ) and you are ??? wondering whats gone wrong. You check your credit cards etc to find that nothing unusual has happened so you think its fine.
Remember most online shops just want a bank account set up for the DD.. they dont all want it to be the address of the place its being sent to. He may have also used your card and its just not showed up yet, this can also happen. The online retailer will just verify the details but not take money so some card issuers will not know its been done.
Next day or even later that day another guy turns up at some silly time while you are hopefully half asleep and claims to be from the courier, they usually have a uniform and some fake but convincing ID and tells you the delivery was a mistake and can he have it back. Most people will happily hand it over.
Now the scammer has a brand new phone that is untracable to him and as long as he changed the EMEI number or flogs it for cash before its blocked he is quids in.
Your dad however will soon get letters from the mobile company wanting to know why he isnt paying for his phone he ordered AND SIGNED for...
Under no circumstances should you ever give back a parcel you have signed for unless you have phoned the company or courier yourself and arranged a return. They will also have a work sheet or label to show you... your mum just gave the phone worth a few hundred quid to a random bloke who knocked on your door.
These scammers often case the house they intend to send the phone to and will use a company that gives AM or PM courier deliveries, they park up and wait till they see the driver drop it off... if he walks back to the van with no parcel they knows its been signed for. Next morning dead early they use their fake badge/uniform for whatever company it was and come calling. They can make it very convincing by describing the driver who dropped it off and what time he dropped it off at. Most people who were suspicious would be concinvced by this and hand it back. They are experianced confidence tricksters and just walk away if its too difficult, they have more lined up.
Good luck with this one.

hopefully i am wrong but it has the signs of this kind of scam.