Depends what the accuser says. They might, being told the suspect's explanation why the items were in his room, say that that is entirely feasible or is correct, they now thought that the goods were not stolen and did not wish to pursue. Then the CPS would not have the suspect charged.
On the simple facts given, this might still be theft . The possession by the defendant of property which he is unlikely to have acquired or have possession of otherwise than dishonestly is sufficient.The circumstances of his acquiring the goods and the nature of them may be enough (even if no loser or owner can be identified and the source of them unknown) If, say, the man lived over a depository and a diamond necklace belonging to a depositor was found in his room, that would be prima facie evidence of theft since there was no reason why he would have it and any explanation given is at least triable as being unlikely to be plausible. Likewise, if he was above a jeweller's and it was no part of his job to have a diamond necklace in his room, for example to work on it, that would be prima facie evidence that he had stolen it.
The mere fact that a complainant does not wish the case to proceed is no reason in itself for it not to. The CPS will decide on the available evidence whether a case is disclosed, whether it is reasonably likely to result in a conviction and whether it is in the public interest to proceed.