Was John the Baptist actually Elijah?

When asked, John the Baptist stated plainly that he was not Elijah returning:

John 1:19  This is the testimony of John, when the Jews sent to him priests and Levites from Jerusalem to ask him, “Who are you?” 
John 1:20 And he confessed and did not deny, but confessed, “I am not the Christ.” 
John 1:21 They asked him, “What then? Are you Elijah?” And he  said, “I am not.” “Are you the Prophet?” And he answered, “No.” 
John 1:22 Then they said to him, “Who are you, so that we may give an answer to those who sent us? What do you say about yourself?” 
John 1:23 He said, “I am A VOICE OF ONE CRYING IN THE WILDERNESS, ‘MAKE STRAIGHT THE WAY OF THE LORD,’ as Isaiah the prophet said.”  

John the Baptist confessed that he was NOT the fulfillment of Malachi 4. Rather, he said his ministry was the fulfillment of a different prophecy found in Isaiah 40, a "voice crying in the wilderness" announcing the Messiah's first coming. Jewish teaching of the day said that Elijah must return before the Messiah arrives, so everyone was looking for Elijah, but the Jews had overlooked Isaiah 40, which foretold that another, unnamed forerunner would come prior to Messiah, and that forerunner was John. So John testified that he was not Elijah; he was the unnamed forerunner of Isaiah 40.

Elijah the prophet has a ministry similar to John when he returns. Elijah is also a herald announcing the coming of Messiah, but Elijah announces the Lord's Second Coming, while John announced the Lord's first coming. Malachi 4 says Elijah will return before the Tribulation (i.e., before the great and terrible "day of the Lord") to announce that the Lord's Second Coming is near. The actual Elijah foretold by Malachi returns to the earth prior to the “great and terrible day of the Lord:”

Mal. 4:5  “Behold, I am going to send you Elijah the prophet before the coming of the great and terrible day of the LORD. 
Mal. 4:6 “He will restore the hearts of the fathers to their children and the hearts of the children to their fathers, so that I will not come and smite the land with a curse.”

The "great and terrible day of the Lord" is a reference to the seven years of Tribulation. So, prior to the start of Tribulation, Elijah will return to the earth. The Lord’s purpose in bringing Elijah back will be to restore the hearts of Israel, which means to bring Israel back to true obedience to the word of God, specifically their Law. 

Elijah’s return is important because during Tribulation Israel will be given an opportunity for a time to worship at a new temple (according to Daniel 9 and Revelation 11). Nevertheless, most of Israel today has little interest in returning to observing a sacrificial system even if a temple were available, so God uses Elijah to prompt Israel’s return to orthodoxy immediately prior to the rise of a third temple.

Therefore, John the Baptist is a type of Elijah. As John the Baptist announced Jesus' First Coming, Elijah will announce Jesus' Second Coming. In that way John the Baptist came in a manner similar to Elijah though John was not the actual Elijah. Jesus confirms that John the Baptist was only a type of Elijah in Matthew 11:

Matt. 11:14 “And if you are willing to accept it, John himself is Elijah who was to come.

Jesus says for those who were willing to accept what John preached, John was Elijah. In other words, Jesus says for the one willing to accept Jesus as Messiah, John becomes that person's "Elijah" in the sense that John was a herald announcing Jesus' first coming like Elijah announces the Second Coming. That person need not wait for Elijah in order to have the Messiah. The person can accept John's testimony instead, and for that person John is their "Elijah."

Jesus was confirming that John was a type of Elijah, though not the actual Elijah. If John were the actual Elijah, then Jesus would not have needed to add the statement, "if you are willing to accept it." If John were truly Elijah, then Jesus would have said John was Elijah regardless of whether someone accepted it or not.