Hi, Jeannine -
Basically the non-conformists were just that: they didn't subscribe to the "conformist" religions of the day such as the Church of England and the Roman Catholic Church.
There are many such groups, the most prevalent being Baptists, Methodists, Presbyterians and Unitarians. Then there are the Seventh Day Adventists, the Wesleyans, Plymouth Brethren and many, many more. One group simply established Independent churches or meeting houses.
The East of England had many non-conformist congregations, many of them Primitive Baptists with travelling preachers and lay preachers.
A Google search will give you far more information than I can squeeze in here!
Best regards
Wendy