What is junk DNA?
The term junk DNA is not used that often in the scientific literature and when it is it is often used very generally, often early in the introduction. It generally refers to any non-coding DNA.
In humans, about 25% of the non-coding DNA is introns and regulatory sequences. These sequences are highly essential for the working of the organism. There are many cases of adaptation from these regulatory sequences (see this answer).
The term junk DNA is very loaded and may make it feel to people that this DNA is not important for the organism survival but this is not quite what was first meant by the term junk DNA. It is true though that repeated DNA such as those in transposable elements are thought to have little impact on the organism phenotype. Transposable elements can however have important role on the evolution of a lineage.
IMO, the claim is false and insulting
By saying things like
They do this because they gave no idea what it does and, from their version of reality, it appears to serve no function., it feels to me that David Icke is using the loaded side of the term junk DNA to insult all geneticist in general.
D. Icke is 1) doing a strawman by suggesting that geneticists think that regulatory sequences are of no use and 2) he is suggesting that geneticists are biased and will invent whatever theory in order to match with a pre-conceived opinion of the reality.
About David Icke
I don't mean to make an intentional fallacy but I would like to note that David Icke is a famous conspiracy theorist who has been illogical and obviously opinion based many times. For example David Icke claims that the moon is actually a spaceship and not a natural satellite (see here). He has made many other fantastic claims of the kind. Scroll down the wikipedia article to enjoy some non-sense!