Here is that passage in the KJV:
Ephesians 2:11-16 Wherefore remember, that ye being in time past Gentiles in the flesh, who are called Uncircumcision by that which is called the Circumcision in the flesh made by hands; That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world: But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ. For he is our peace, who hath made both one, and hath broken down the middle wall of partition between us; Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace; And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby
The thing to remember is that "in time past" there was a "middle wall of partition" between Israel and Gentiles, and the Gentiles were "aliens." That does not mean that God did not have a plan for Gentiles, etc. In "time past," Gentiles were without direct hope. God's chosen vessel in dealing with man was Israel. Gentiles had to approach God indirectly through Israel (i.e. "bless them that bless thee" etc). So in simplistic terms, this is how the middle wall of partition worked:
God/Christ <---> Israel <---> Gentiles
This divine order can be seen and demonstrated in the Old Testament. So your question is when did things change? More directly, what your question concerns when did the middle wall of partition "fall" and/or when was it revealed that it fell. What about the time period before the cross and the earthly ministry of Christ? Was the middle wall of partition up then? Often unrecognized is the fact that there are only TWO recorded interactions of Christ with Gentiles. Both of these interactions clearly demonstrate that ("at that time") Israel was the vessel between Christ and the Gentiles, and that the middle wall of partition was still up.
GENTILE INTERACTION #1 - A Gentile Approaching Christ in the Correct Way
Luke 7:2-9 And a certain centurion's servant, who was dear unto him, was sick, and ready to die. And when he heard of Jesus, he sent unto him the elders of the Jews, beseeching him that he would come and heal his servant. And when they came to Jesus, they besought him instantly, saying, That he was worthy for whom he should do this: For he loveth our nation, and he hath built us a synagogue. Then Jesus went with them. And when he was now not far from the house, the centurion sent friends to him, saying unto him, Lord, trouble not thyself: for I am not worthy that thou shouldest enter under my roof: Wherefore neither thought I myself worthy to come unto thee: but say in a word, and my servant shall be healed. For I also am a man set under authority, having under me soldiers, and I say unto one, Go, and he goeth; and to another, Come, and he cometh; and to my servant, Do this, and he doeth it. When Jesus heard these things, he marvelled at him, and turned him about, and said unto the people that followed him, I say unto you, I have not found so great faith, no, not in Israel.
In this account, notice how the Gentile does not seek out Christ directly. He approaches indirectly through Israel. Israel then in turn, presents him to Christ, explaining his worthiness as a Gentile - i.e. he blessed Israel and recognized their God as the true God by building them a synagogue. Christ recognized this Gentile's correct approach of going through Israel and blessing them, as well as other details of his faith and knowledge.
GENTILE INTERACTION #2 - A Gentile Approaching Christ in the Incorrect Way
Matthew 15:22-28 And, behold, a woman of Canaan came out of the same coasts, and cried unto him, saying, Have mercy on me, O Lord, thou Son of David; my daughter is grievously vexed with a devil. But he answered her not a word. And his disciples came and besought him, saying, Send her away; for she crieth after us. But he answered and said, I am not sent but unto the lost sheep of the house of Israel. Then came she and worshipped him, saying, Lord, help me. But he answered and said, It is not meet to take the children's bread, and to cast it to dogs. And she said, Truth, Lord: yet the dogs eat of the crumbs which fall from their masters' table. Then Jesus answered and said unto her, O woman, great is thy faith: be it unto thee even as thou wilt. And her daughter was made whole from that very hour.
In this account, notice how the Gentile woman seeks out Christ directly, the incorrect way. She approaches him, and what did the Lord Jesus Christ do? "But he answered her not a word" and IGNORED her. Why IGNORE her? Because Gentiles were to go through Israel, which is why he also stated "I am not sent but unto the lost sheep of the house of Israel." But something needs to be noted. Israel was failing in their responsbility. She did initially approach in the correct indirect way, but Israel apparently didn't want to deal with her (i.e. "she crieth after us") which was their role. They were ignoring her. Though Christ didn't answer her, and then stated he was sent only to Israel, the Gentile woman persisted. Christ then used an analogy of the divine order (i.e. God/Christ <---> Israel = "children" <---> Gentiles = "Dogs"). Like the centurion's servant, she demonstrated her clear knowledge of the divine order by stating that God's blessing goes to the gentiles ("dogs") through Israel. She understood the analogy, and iterated her position of being secondary to Israel. Christ recognized this Gentile's faith and knowledge of going through Israel.
In the "time past" of the Old Testament and the earthly ministry of Christ, Gentiles were concluded in unbelief and God set apart the nation Israel, which was his revealed purpose. When Israel proved themselves unworthy, stumbled and fell, God then revealed his hidden purpose through the Apostle Paul where he concluded all in unbelief (Romans 11:32), both Jew and Gentile.
Ephesians 2:13-16 But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ. For he is our peace, who hath made both one, and hath broken down the middle wall of partition between us; Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace; And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby
Also commonly unrecognized is that the Apostle Paul is the ideal representative of the body of Christ, and the breaking down of the middle wall of partition, as Paul was both a Jew and a Roman citizen (Gentile rights).
Hope this helps...