Nobody really fought in full armor at that point, as far as I am aware.

However, two cavalry regiments that I am aware of (Both on the Parliamentary sides) fought in something close to full armor : three-quarter-armor, which covered almost all of their body except for their feet. Instead, they wore long boots. They were referred to as "cuirassiers".

The more famous of the two regiment was known as the "London Lobsters" due to their armor. The other regiment were called "The Earl of Essex's Lifeguard". Their armor would have looked something like this and would have been quite heavy - even up to 80 pounds.

It provided protection from bullets, but also was expensive and impacted mobility. One member of the latter regiment noted that after he dismounted, "I could not without great difficult recover on horse-back again, being loaded with cuirassiers' arms."

The men of these regiments were not Knights, but probably came from fairly high social status (Early in the war, troops were expected to provide their own mounts, which would be a considerable expense).

Officers or Commanders of other regiments sometimes equipped themselves in near complete armor. They are probably the closest thing to knights in full armor during the English Civil War, but that is a matter of debate.

Sources:

royalarmouries.org

The English Civil War, 1642-1651: An Illustrated Military History