The concept of popular sovereignty espoused by the Americans was mainly radical in how far they were willing to take it. The idea of government by the consent of the people was not terribly radical. But a government that was based only on the consent of the people was radical.
Britain was a fairly democratic country in these times. However, it was not nearly as democratic as the United States was to become. First of all, it had a king as the head of state. The king did not rule by himself, but he did have power. Second, the British Parliament included a House of Lords that was not elected. Between them, the king and the House of Lords meant that the British system was not completely democratic.
The Americans, by contrast, envisioned a much more democratic system. They envisioned a system without a king and without an aristocratic branch of government. Therefore, they were radical in that they believed in the idea of a system of government where the people had control of the entire government and no part was selected based on hereditary considerations.