This is an absolutely absurd restriction for moving traffic. Somebody could be in his way home from France to Scotland and would have no idea whatever about "event days".
Actually they damn themselves in their reply, by saying you must go and look on their website, and also, as 'Stamfordman' points out, look out for a sign giving the dates when this is not a traffic sign. Motorists are under a duty to obey traffic signs, as listed in the TSRGD, and nothing else. If they wanted to show Event times for the bus lane, then the actual bus lane signs should show them, but again, this would not be a traffic sign.
Your case really needs to be taken to London Tribunals where I'm sure you will win, not least because you can insist that the person who signed the video record attends the hearing. They never do.