Yes, but it was precisely in Scotland that such a moderate current of Puritanism as Presbyterianism was "founded." The founder was John Knox, a student of Jean Calvin. The main requirement was the replacement of bishops with elected presbyters. In 1592, Presbyterianism was recognized as the state religion of Scotland, although it had enjoyed great popularity long before then.
In England, however, this current gained its strength only with the start of the revolution. And even though they were moderate monarchists, from the point of view of religion specifically, they were for a "cheap church," i.e., Protestants.