In my own field of study, I see Elizabethan authors such as Smythe and Silver seeming to argue in favor of 'native' or 'ancestral' 'English' methods of fighting - the longbow and sword and buckler, for instance. Did this sentiment reflect a rising English nationalism or sense of 'English-ness'? I know about of the popular reputation of the History Plays of Shakespeare as nationalistic, and some of the pop history around Elizabeth, but to what extent is that reality and to what extent is that an anachronism?
Elizabethan England, was at the very least, a society with a flowering sense of patriotism and self-regarding pride. Whether it should strictly be called nationalistic depends on one's perspective on what a nation and nationalism is. Various authors have argued that the modern nation-state and nationalism was invented in early modern England, for example Hans Kohn in 'The Idea of Nationalism: A Study in Its Origins and Background', and Liah Greenfeld in 'Nationalism: Five Roads to Modernity', and that it served as a prototype for later developing nations like France. 'Modernists' like Eric Hobsbawm argue that nations and nationalism exist only in the post 1789 period, but even Hobsbawm ascribes 'proto-nationalism' or 'modern patriotism' to Tudor England.
The reasons for this rising patriotism / nationalism in this period are the increasing power of the state, the fact that the reformation in England had had the outcome of fusing religion and state into one, and the increasing prominence of England in many fields like trade, science and culture. This can be traced all the way back to the hundred years war, which cut off most of the French domains of the English Kings, and the subsequent wars of the Roses, which Greenfeld argues decimated the feudal elite, leading to its replacement by an official elite at the top of the social hierarchy. We have increasing centralisation and reduction in the power of the nobility under Henry VIII, and then under Henry VIII the break from Rome, the printing of the English bible, and the establishment of the monarch as head of the church. "This realm of England is an empire" as the 1532 Statute in Restraint of Appeals put it. Greenfeld writes that "By the 1530s the idea of service to the nation had entered, or at any rate was entering, the discourse, as was the concept of England as a separate entity and as a polity which was not simply a royal patrimony, but commonwealth."
After the attempted reintegration with Catholic Europe of Mary's rule, the Elizabethan era saw the full flowering of this patriotic spirit. You've mentioned Shakespeare's plays, which display numerous instances of patriotism, and Elizabeth herself, to answer questions about why she was not married, stated "l am already bound unto an Husband, which is the Kingdome of England, and that may suffice you".