In the Regency period, the ideal was pretty clean-shaven. Mustaches were considered to be have foreign Continental European or military connotations, or to be an affectation of those few foppish individuals who aped continental Europeans and/or military officers. Beards were almost considered outlandish (only a few elderly poor or insane or invalids had them, and they were not at all a common sight in public).

Here's a Feb. 26 1824 caricature by W. Heath, "Corinthian Steamers, or Costumes and Customs of 1824", which shows the very beginnings of the transition from Regency to Victorian with respect to facial hair and smoking (both of which were considered outlandish and un-English during the Regency, and are ridiculed here, but later would come to be considered highly respectable during the Victorian period):

Dialogue:

Flaming dandy (2nd from left):

"Fire! Fire! oh Dear, my best Mustacios will be quite Destroyd!"

Alarmed dandy (next to left):

"Fire! Fire!"

Irish fireman (at left):

"My Master, I must fetch our Engine to put out your Steam Engine"

At the right of the image a dandy is blowing smoke in a lady's face, in flagrant violation of the etiquette of the time (in which smoking was mostly not done indoors at all, and never in the presence of ladies). Caption is "Fond of Steaming Ladies! do you smoke it, eh!" (The steam engine was a shiny new technology in 1824, so smokers are jocularly compared to steam-engines.)