A consort was a term used for an ensemble consisting of members of the same instrument family. So one could have a consort of gambas, a consort of lutes. A mixed consort consisted of instruments from different families.
These ensembles were very popular in Elizabethan times, sixteenth and seventeenth century England. They were highly popular among aristocratic families, and were in that sense an early form of chamber music: you bought the sheet music and the instruments, and you could play these works with your family.
John Jenkins was born in 1592, but was most active during the Civil War (1642-1651) when he was presented with the opportunity to write these household pieces. John Jenkins is also a player of American football and a maker of glassworks. Let’s assume I got the right one here.