A couple of days ago I found a cassette of the type it would have been on - A BASF C60 with a red label - and put it in the old radio cassette player. It proved to be the right tape. As suggested by cleanskies I tried Shazam and it texted me that it was 'Spring High' by Ramsey Lewis. In the way of things a video of a picture of the album cover along with a recording can be found on YouTube here. My cassette recording of it starts at about 17 seconds in which is, I think, interesting as I don't think the first 17 seconds are particularly good. Whether I didn't record them because of this, or whether I don't like the beginning because I was used to hearing it without I am not sure. Of course, the journey is more exciting than the destination, but it is nice to know what it is. I have to say that some random YouTubing does not really encourage me to go out and find more of his work.
Also on the tape was Running Man by Al Stewart (YouTube here). This was recorded off a land-based pirate, with a certain amount of FM hiss. At the end is a jingle from the station, something I don't remember at all called Parkside Radio, parodying one of the jingles of Thameside Radio. Ah, the late 70s / early 80s London Sunday land-based pirate, rather white and geeky, where I think I first came across Steely Dan and The Alan Parsons Project. London FM, Thameside Radio, The Intrepid Birdman, isn't it? Small boys, FM transmitters for goal posts.
The song itself is a song with an inconclusive narrative, the equivalent of the InterZone 'mood piece'. I think of it as being vaguely SF-nal but I suppose it isn't really. Listening to it on YouTube, I see that some of the treble heavy tonal quality (there is a word I want to use but it escapes me) I imputed to it being recorded off the pirate radio may be in the track itself, but it sounds wrong without the hiss.
I must have listened to that tape hundreds of times. As I've said before, it is hard to imagine anything sounding as new and exciting as things did then.