And there they were.
The episode in particular of The New Avengers from which this titles clip was pulled is "Angels of Death". For you trivia junkies: This installment was directed by cameraman Ernie Day (A Passage to India) and co-written by Terence Feely, who wrote arguably Space: 1999's best episode, the satisfyingly pulpy two-parter "The Bringers of Wonder".
Composer Laurie Johnson reworked his Avengers theme for this new version; something that disappointed me when the series premiered as I had his original tune burned into my brain. The update title music lacked the romantic and exotic punch of the original, and took on an almost incongruous martial sound. A minor quibble, yes.