Methodism was born out of the revivals of John Wesley and George Whitfield who were both Anglicans in America. Whether or not they maintained a relationship with the Church of England, it seems like they could have easily established churches of the Evangelical Free Church model if they were going for a version of evangelical Anglicanism with a congregationalist polity. Why a new denomination?
Wesley and Whitfield were Englishmen, and staunch members of their national Church. Wesley spent two years in America. Whitfield made prolonged visits to America on seven occasions, and died during his last. Likely they could, if they had wished, have founded churches with a congregational polity, but nothing could have been further from their minds. Wesley was not a denominationalist, never mind a congregationalist.
Methodism was a movement and Society within the Church of England, not a rival to it.Methodist meetings were never timed to coincide with services in the parish Church, and members were strongly urged to attend both, and certainly to take Holy Communion in the C of E. Methodist leaders, unless episcopally ordained in the Established Church, were known as lay preachers, and never presided at Communion.
Not only did Wesley believe schism was evil in itself, he believed it would be disastrous in practice. For Methodists to leave the Church would be "like throwing balls of wildfire", stir up bitterness, split Methodism, hinder preaching, consume and waste time and energy and deny people the chance to hear the gospel.
It was developments in America which led to the Anglican Methodist split.
Firstly, the Church of England was never ubiquitous in America, as it is in England. Secondly the Oath to the King led many clergy to leave the U.S. for England, Canada over American Independence. Thirdly was the fact that there were no bishops in America. Episcopal Ordination involved travelling to London, whose bishop was responsible. After 1776 American citizens were not able to swear loyalty to the King, and the Bishop of London was unable to ordain them unless they did.
There were not enough priests/presbyters and no way to get more. According to Anglican/Methodist understanding Holy Communion could only happen with an episcopally ordained priest/presbyter. This was the Sacramental Crisis. Of course, the impasse was eventually resolved, but in the meantime John Wesley came up with his own solution.
Searching the Scriptures, and the Continental practices, he became convinced that it was not true that only a bishop could appoint a presbyter. Any presbyter could appoint others. He therefore appointed some for America, and they began celebrating Holy Communion.
Methodism went on to become the largest denomination in the US.
Following Wesley's death in 1790, English Methodists decided to follow where America had led. The lay preachers, some, were ordained by the Methodist Connexion, without bishops, and celebrated the sacraments. Methodism had become a denomination.
The American Revolution caused a major shortage of priests so the Wesley gave preachers the power to ordain sacraments much to the disliking of the Anglican Church, so after Wesley died the Anglican and Methodist Church split. Here's a link to Wiki Article on it https://en.m.wikipedia.org/wiki/Methodism hope it helps 😊