:"Is it possible to transfer app purchases between two different accounts?"
"I trashed my old account as my iPhone was stolen. "
Why would you do that? Just change your password.
". Unfortunately I cannot update my apps as it says that I'm on a different account."
because you started a new account. not sure why you would do that.
"Any idea how?"
You would have to sign into the old account in order to upgrade. This is why you don;t go creating new accounts when you can just change your password.