Hm, you sure it was just 20-30 metres, it looks longer in the video ? Anyway, it seems a fairly obvious contravention. Any reason for entering the lane early ?
If you are prepared to take them all the way to London Tribunals, our Hippocrates has developed a winning appeal based on a clause in the 1996 Act which is shown at the top of your PCN, but I'll let him explain it. But first you must submit representations to Greenwich against the PCN. I wouold suggest that these be based on only driving in the buslane for a very short distance in order to turn left. They will, of course, refuse these.