Huldrych Zwingli reached the regulative principle first, working through Zurich's churches in the 1520s and removing organs, images and the Mass itself on the ground that Christ had commanded a specific form of worship and nothing beyond it. John Calvin took up the same logic in Geneva a decade later, arguing that God alone has the right to prescribe how he is worshipped, a case he presses at length in the opening book of the Institutes. Where the Lutheran and later Anglican reformations kept whatever medieval practice Scripture did not explicitly forbid, the Reformed and Presbyterian churches removed whatever Scripture did not explicitly warrant.
The English and Scottish Puritan movements inherited the principle and turned it against the surviving ceremonial of the Church of England: the sign of the cross in baptism, kneeling to receive communion, the wearing of vestments, a fixed liturgy read rather than a sermon and prayer offered freely. The argument ran through the reigns of Elizabeth, James and Charles and fed directly into the calling of the Westminster Assembly in 1643. The Assembly's Confession of Faith states the principle formally in its chapter on religious worship and the Sabbath day, and its companion Directory for Public Worship, published in 1645, set out what a Reformed service should contain in place of the Book of Common Prayer it was meant to replace for Parliament's Puritan allies.
The principle did not end the argument between Reformed Christians and their neighbours; it relocated it inside the Reformed churches themselves. Every subsequent dispute over an element of worship, an instrument, a hymn, a form of prayer, has had to be fought on the same ground since: not whether Scripture forbids it, but whether Scripture commands it.