So the general answer is indeed 'iron and steel', as you said, but that isn't very interesting or informative. Fortunately, Alan Williams has written 900+page book, the Knight and the Blast Furnace, on this very subject, and I take a lot of this answer from Williams' scholarship The period that you choose is actually one that has a tremendous amount of change in European Metallurgy and the metallurgy of armour in particular, so this answer is going to vary somewhat depending on when we are talking about. Moreover, we have very little English armour surviving from before 1520 or so, and that which does survive is almost all helmets used as 'funerary achievements' in churches, many of which may not have been made in England. Even after 1520, our sampling of English armour is heavily skewed toward the very highest end - the products of the Royal Workshop at Greenwich, which came from a -very different- metallurgical tradition than the 'native' English armour made in London (or in much, much smaller quantities in places like York - as elsewhere in Europe armour production was fairly centralized). However, we also know that the native armour production of England didn't account for a lot of the armours actually worn in England - armours worn by English knights might be made in Flander or as far away as Milan. So there is a lot of uncertainty about what 'English' armour was like, metallurgically, because our sample sizes are small and even then hard to interpret. Indeed, when we talk about the armour worn by English knights and not English-made armour, we must remember that a lot of armour wouldn’t have been made in England! I talk a lot about the European armour industry here:

• Manufacturing and Supplying the Armour of Weapons of a Late Medieval Army

• Why were Milanese armourers so successful?

• The Armour Industry of Milan, contd.

• Manufacturing Munition Armour

• What did Royal Armour Look Like?

• Two Podcast Episodes About the armour industry

So first, terminology. Wrought iron is pure iron - little to no carbon, maybe some naturally occurring impurities, but basically no carbon. Steel is an allow of Iron and Iron Carbides that together form a crystalline matrix that makes it harder than wrought iron, and these crystalline structures can be made even harder by heat treatment - heating and then cooling the metal - indeed, wrought iron is softer than bronze, whereas steel can be significantly harder if it is heat treated. Steel can be divided into low carbon (under .3% or so), medium carbon (.3%-.6% or so) and high carbon steel. Cast iron, weirdly enough, has even more carbon than steel (over 2%), to the point where it is rather brittle (think of a cast iron pan), and it wasn't used for armour in Europe. Regarding alloys, medieval steels are generally a basic 'carbon' steel. Some European iron deposits naturally have maganese, which is a common alloying element in modern steels, but this wouldn't be deliberately added to steel after the fact.

I talk more about the metllurgy of medieval armour here:

• From Ore to Harness: The Steps of Manufacturing Plate Armour

• The Importance and Illusiveness of 'Good Steel' in Medieval and Early Modern Armour

In very large, macro terms, what we see in medieval armour from the high middle ages to the late middle ages to the early modern period is an improvement in metallurgy - less iron, more steel, better carbon content, more heat treatment - from the 14th through the later 15th centuries, and then in the later 16th and 17th centuries the displacement of steel by wrought iron as more and more armour becomes cheaper and arguably worse in quality. However, this is a very broad view mostly looking at the armours that survive - and those are mostly German or Italian armours, not ones made in England or elsewhere. Moreover, the regional view is actually more complex - Italians and Southern Germans seemed to use a different form of heat treatment (a slack or interrupted quench for the Italians, a full quench for the Southern Germans), and they develop these at different times (14th century in Italy, mid 15th century in Southern Germany). Moreover, even very good, heat-treated armours might have different carbon contents - for heat treatment to work steel needs to have a medium carbon content of .3-.6%, so a low carbon steel will not 'take' the heat treatment. The view of the metallurgy of armours outside Southern German Lands (Frankonia, Bavaria, Tyrol) and Northern Italy (Milan and Brescia, both in Lombardy) is murkier because so little survives. Surveying the armour of Flanders, North Germany, Spain and England, Williams didn't see as much evidence for heat treatment, but the sample sizes are so small that I wouldn't necessarily make a conclusion from that. We know that the Flemish armourers of King Henry VIII brought troughs for quenching, and we have French town regulations from Angers calling for hardening the plates of brigandines in the 15th century.

With that said, the evidence for hardening in English armour outside of the Greenwich workshop of Henry VIII is spotty. Some of our earliest pieces were at least attempted to be hardened, but many other pieces appear to have been air cooled. With that said, we’re talking about a sample size of 7, compared with much larger sample sizes of Italian and South Germany armours from the same periods. So again, I would caution against drawing a definitive conclusion. Only one of these helmets was wrought iron, which is in line with armour from other parts of the Europe in the 14th and 15th centuries - wrought iron armour is not common and becomes less common over time. Williams did not test any English armours from the later 15th century or the 16th century, so the rest of this answer is somewhat more specifically focused on the Greenwich court armoury of Henry Viii. This was one of a number of court armouries founded in the 16th century - rather than simply appointing existing workshops as court armourers, princes began to build their own armouries, supply them and directly pay their employees - the trendsetter here was Maximilian I of Burgundy, Austria etc etc, who founded an armoury at Arbois in Burgundy and then one in Innsbruck as well as patronizing existing independent masters. Tobias Capwell has suggested that it was a desire to follow Continental fashions and set aside the provincial styles of English armour that led Henry VIII to hire various Flemings, Italians and eventually South Germans to serve as court armourers in Greenwich, so at least at first the armour of the Greenwich workshop may not have been much better than that of London armourers, or perhaps not even as good. Indeed, no surviving pieces from the early period are successfully heat treated, while hardening becomes more successful in the 1540s. It isn’t until the Elizabethan period (when native English armourers trained under the ‘Almains’ take over) that we see routinely successful hardening. Ironically, this flowering of armour metallurgy occurs just as armour in the rest of Europe is declining in quality (metallurgically and arguably artistically) - by the 1570s only Augsburg masters and the Greenwich workshop are routinely heat treating armours. So an Elizabethan courtier armed in a Greenwich harness as a sign of royal favor would be among the best armoured soldiers in later 16th century Europe. But he would be a lucky indeed - unlike the Innsbruck workshop of Maximilian, which both mass produced armour and produced luxury harnesses, Greenwich exclusively produced luxury armours for royals and court favorites, so even as the Medieval man at arms gives way to the early modern curassier the average English armoured horseman would probably be equipped with armour made in London or in armour imported from Flanders or Northern Germany, just as many of his predecessors would have worn harnesses from Milan or Flanders.

Speaking of these imported armours, the metallurgy of Flemish armour is similar to that of English armour - often lower carbon steel, without successful heat treatment, but the sample size Williams tested was still small. Italian armours from the 15th century are a different story. Those with Armourers marks are generally heat treated and often made of medium carbon steel, while unmarked armours are of less consistent metallurgical quality. The marked armours would be more expensive and so more likely to be purchased by a wealthier man at arms, while unmarked armours would be cheaper.

So to return to your question, 'knightly' armour worn in England was generally steel, sometimes hardened steel. It was rarely a simple wrought iron, at least until the early modern period.