Have knights from the  Danish Order of Knighthoods ever fought against English Knights?

It is possible that individual knights from the Danish Order of Knighthoods and English knights may have fought against each other in various historical conflicts.

However, it is important to note that the Danish Order of Knighthoods is a modern Danish honorific order, established in 1671, and is not directly related to historical Danish knights who may have fought against English knights.

Additionally, the term "English knights" is quite broad and encompasses many different individuals and periods of history, so it would depend on the specific context and time period being considered.

What periods are they most likely to have fought in, please?

Historically, there have been several periods of conflict between Denmark and England where knights from both sides may have potentially fought against each other.

One such period is the Viking Age (793-1066), during which Danish Vikings conducted raids and established settlements in England, leading to frequent conflicts between Danish and English forces. 

Knights, as heavily armoured and skilled warriors, would have likely played a significant role in these battles.

Another period of conflict between Denmark and England was the 16th and 17th centuries, when the two countries were involved in a series of wars, including the Anglo-Dutch Wars and the Scanian War.

These conflicts often involved naval and land battles, with knights potentially fighting on both sides.

It is important to note, however, that the use of knights as a distinct class of warrior declined in Europe over time, and by the 17th century, the role of the knight had largely evolved into that of a ceremonial honorific title rather than an active military role.