The suit of armour that you're referring to is a suit of tournament armour, and would never have seen actual use in battle. For this reason, they're typically a touch thicker than most combat armour and a fair bit heavier as well. They were also never mass produced because the customer base for such armor is tiny. If you're interested in mass produced arms and armour from the medieval and early modern period, I suggest researching "munitions armor."

Regarding the specific suit you mentioned, you may notice that it does not protect the inside of joints (armpit, neck, back of knee and inside of elbow) with chainmail, but rather with solid plates, called lames, that overlap and slide against each other. This particular method of protecting these areas is extremely difficult to produce and requires an incredible amount of work on the armourer's part.

That said, if you just want armor that does head to toe coverage, including joints, that's basically most suits of armor since the 13th century onward. The key visual difference is that significant areas will be protected with a chainmail sleeves, skirts and "voiders."

Sources:

Archaeology of Weapons by Ewart Oakshotte

Arms and Armour of the Medieval Joust by Tobias Capwell

Masterpieces of European Arms and Armour in the Wallace Collection by Tobias Capwell, David Edge, and Jeremy Warren

Armour of the English Knight, 1400-1450 by Tobias Capwell

To add to what u/Daedalus1570 says above, the kind of armour that Henry VIII had made (but was not finished) in 1520 was a foot combat armour for individual, dismounted combat in a tournament setting. Generally such a combat would be fought with pollaxes but other weapons might also be used, such as Estocs (specialized thrusting swords designed to pierce the gaps in armour). As such, they are kind of the foot-combat equivalent of a specialized jousting armour for the joust of peace, though they resemble war armour somewhat more closely. 'Tournament' features for this armour include the great bascinet (no longer used in war armours for more than 60 years before this armour was made, common in foot combat armours because against a single opponent you don't need to turn your head as much) and the symmetrical pauldrons (which you also see on some war armours intended for use on foot in the 15th century) as well as the complete coverage, which makes the armour unusable when mounted. And that uselessness for mounted combat is the most important part - even earlier war armours 'optimized' for fighting on foot, like English armours from the middle of the 15th century, -can- be used on horseback, because in the end war harnesses need to be versatile (because real battles are not predictable things). So these armours were restricted to tournament foot combats. Moreover, having specialized tournament armour means being able to afford multiple armours, which is one reason why tournaments are more socially restricted, generally, than fighting in full harness in war is - there are a lot of lesser aristocrats that can afford one armour but not 3. However, even in the context of foot combat this kind of armour only had a brief fashion in the years around 1520 - there are only 3 full and 1 partial harness in this style that I know of. Put simply, this armour is so intricate and specialized that only the wealthiest princes could afford it. Far more common were 'tonlet' armours, which have a long skirt (far longer than the usual fauld, going down nearly to the knees rather than the upper thighs and flairing more) which gives much the same protection without having the fiddly bits over the butt. Moreover, if you swap out the pauldrons and take off the long tonlet of a tonlet armour you can have a usable field harness, which made tonlets a common part of the 'garnitures' (mix and match sets of armour) that became luxury status symbols in the 16th century.

This particular armour was made for the Field of the Cloth of Gold and never used, because the rules were changed to specify that the combatants had to use tonlets, the much more common form of foot combat armour from the late 15th century until the later 16th (when you see more foot combat at the barriers). To conclude, the armour is actually incredibly rare as a survival, and was rare at the time. It was a luxury sporting armour for kings, not an armour that was ever suited for mass use.