Quoted: In British English -- or so I believe -- sometimes the practice is the opposite: the British might say "I gave it him" -- where "it" (the direct object) comes first.
It would be "I gave it to him" in Standard British English.
In some regional British accents, say Yorkshire; then the "to" might be dropped, as it is implied.
Your other sentance "I gave him a spoon." would also pass as Standard British.
(Though more commonly you'd hear: "I gave a spoon to him" or "I have given him a spoon")