As far as the law is concerned with regard to holding onto, or disposing of, the guy's belongings, it's the provisions of the Torts (Interference With Goods Act) 1977 that apply, with you being the 'bailee' and your former tenant being the 'bailor':
"If the bailee—
(a) has in accordance with Part II of Schedule 1 to this Act given notice to the bailor of his intention to sell the goods under this subsection, or
(b) has failed to trace or communicate with the bailor with a view to giving him such a notice, after having taken reasonable steps for the purpose,
and is reasonably satisfied that the bailor owns the goods, he shall be entitled, as against the bailor, to sell the goods".
http://www.legislation.gov.uk/ukpga/1977/32
So, once you've 'taken reasonable steps' to try to trace the guy, you can then sell the stuff he left behind. You're obliged to retain the proceeds of such a sale, less any expenses of that sale, and pay them to the 'bailor' upon demand.
You could probably show that you'd 'taken reasonable steps' if you were able to prove (e.g. through copies of correspondence) that you'd asked the relevant agencies (DWP, etc) if they were prepared to forward a letter to the guy if you provided them with a stamped envelope. (They'd almost certainly refuse to do so but that wouldn't matter as you'd then have proof that you'd tried to 'take reasonable steps' to trace the guy).