James May's Cars of the People: Music Identification Thread

Hello all, sorry for the thread bump. I'm new here but was re-watching an old episode or two of Cars of the People just now and have found this thread while searching for information - I just had to sign up, because there's a piece of music I've been wanting to get hold of for ages but I don't know what it is. It's in episode 1 of series 1, at about 15:30. Sounds like something from the late 60s, but I really have no clue what it is. Any help would be greatly appreciated!
Listen to the Flower People by Spinal Tap, from the movie This is Spinal Tap - which is very funny

- - - Updated - - -

The music from the Countach section I have collated:

(DIFFERENT license-free music is used on the BBCworldwide videos of this part on youtube)

in order of appearance:

something by Guns and Roses

Club Tropicana - Wham!

99 Red Balloons - Nena

something ?

Jan Hammer - Miami Vice theme

something, I think by Duran Duran at 28:11 - what?

Batdance - Prince

Jump - Van Halen

The Flaming Lips - Bad Days

Huey Lewis and the News - Back in Time (from BTTF)

and if you like VERY 80s synthpop - try this https://www.youtube.com/watch?v=rDBbaGCCIhk
This was killing me for days. Virtually NOTHING got done but at last - The Countach part is:
Corey Heart - Eurasian Eyes!

The phrase we've been hunting for is not actually "in the wildest co..." but rather "...when the world is cold"

So, there you have it ;]

Hi, I'm just so desperate now... can't get over it. Looking for kind of instrumental song in S2E2 at 56:10 for a while but unfortunately no luck at all. Can someone help me find this little piece of art, please?