Not only does Acts 15 show that the leader of the Church was James, the brother of Jesus in Acts 15, but Eusebius, the early church historian does also. After his death, James was succeeded by Symeon, another relative of Jesus. The Church was always headed by a Desposyni, a relative of Jesus, not one of the apostles.
"After the martyrdom of James and the capture of Jerusalem which instantly followed, there is a firm tradition that those of the apostles and disciples of the Lord who were still alive assembled from all parts together with those who, humanly speaking, were kinsmen of the Lord - for most of them were still living. Then they all discussed together who they should choose as a fit person to succeed James, and voted unanimously that Symeon, son of the Clopas mentioned in the gospel narrative, was a fit person to occupy the throne of the Jerusalem see. He was, so it is said, a cousin of the Saviour, for Hegesippus tells us that Clopas was Joseph's brother.
Under the reign of Domitian, the same emperor ordered the execution of all who were of David's line, and there is an old and firm tradition tat a group of heetics accused the descendants of Jude - the brother, humanly speaking, of the Saviour - on the ground that they were of David's line and related to Christ Himself. This is stated by Hegesippus in so many words:
And there still survived of the Lord's family the grandsons of Jude, who was said to be His brother, humanly speaking. These were informed against as being of David's line, and brought by the evocatus before Domitian Caesar, who was as afraid of the advent of Christ as Herod had been. Domitian asked them whether they were descended from David, and they admitted it. Then he asked them what property they owned and what funds they had at their disposal. They replied that they had only 9,000 denarii between them, half belonging to each; this, they said, was not available in cash, but was the estimated value of only thirty-nine plethora of land, from which they raised the money to pay their taxes and wherewithal to support themselves by their own toil.
Then, the writer continues, they showed him their hands putting forward as proof of their toil the hardness of their bodies and the calluses impressed on their hands by incessant labour. When asked about Christ and His Kingdom - what it was like, and where and when it would appear - they explained that it was not of this world or anywhere on earth, but angelic and in heaven, and would be established at the end of the world, when He would come in glory to judge the quick and the dead and give every man payment according to his conduct. On hearing this, Domitian found no fault with them, but despising them as beneath his notice let them go free and issued orders terminating the persecution of the Church. On their release they became leaders of the churches, both because they had borne testimony and because they were of the Lord's family; and thanks to the establishment of peace they lived on into Trajan's time. So must we learn from Hegesippus."
Eusebius describes Peter as the leader amoung the disciples of Jesus and the principal apostle.
So as you can see Peter was the head apostle, but the Desposyni were the heads of the whole Church.