My answer would be highly unlikely, because of the reasons I outline below.
I argue that the reason why the English and Scottish were generally of a Calvinist nature has to do with the Lollards back in the 14th and 15th centuries. When you examine the theology of the Lollards they are the direct ancestors of the English puritans in the 16th and 17th centuries.
It was notable that the Scottish Reformation was Calvinist in flavour and the Lowlands of Scotland (expecting those areas which still spoke Gaelic) were pretty much of the same culture as the Counties of England north of the Humber.
There is little doubt Edward VI if he survived would have turned the Church of England into a Calvinist in practice as well as theology (The Thirty Nine Articles are generally Calvinist). Likewise for an Elizabeth I if she had been Puritan theologically. Also if England had remained an official Roman Catholic nation there would be a sizeable Calvinist minority with more influence than their numbers were. Because they would concentrated in London and the South-East. Depending on which monarch is ruling in the late 16th century an English war of religions could be possible.