There were people who were Calvinist to one degree or another all over Europe by the Elizabethan era. During that time, much of England was to some extent Calvinist.
For example, during Elizabeth's reign, the Church of England was doctrinally Calvinist. The Anglicans believed in predestination and were very anti-Catholic. But there were others in England who were even more radical in their Calvinism. These were the Puritans. The Puritans felt that the Church of England was still too much like the Catholic Church and that it still needed to be purified of those Catholic influences. Both the Anglicans and the Puritans, then, could be called Calvinist, but they did not agree with one another even so.
So, by Elizabeth's reign, Calvinism was well established all over Europe. There were Huguenots in France, and Calvinists in Germany. There were Knox's Presbyterianism arising in Scotland. As I said before, most of England was to some degree Calvinist.