In most of Europe the year ran from about 1 April to 31 March until early modern times. If one wants to be really pedantic one could say "Elizabeth I came to the throne in November 1558-9 [that is, 1558]".
Nevertheless, I'm surprised that people didn't find it odd that the year didn't change when the numeral did ... - in other words, the idea that all that happened to the date on, say, 1 January 1575 was a mere change in notation from 1574 to 1575.