@libertybonds you could possibly have cause to complain about the bus lane one if it really isn't well sign-posted/labelled but if you crossed a solid white line to enter the lane, then that should have been a clue. Most bus lanes (if not all?) are denoted by a solid white line and the rule is to never cross one.
If you'd be happy to share which junction it was someone either local may come along and advise, or we could look on Google.
I think you've probably realised you're bang to rights on the box junction one though. If you can't see in front of the vehicle in front of you, you should hang back before entering the box junction to ensure your route out of it is clear.
The penalties do seem pretty steep though, so I'd see if they reduce them by 50% for prompt payment at least. This would suggest it is - Waltham Forest website
I remember being in the car with my DP and he had a turn left after a bus lane. He nipped in to the bus lane about 5m before it ended and I remember thinking at the time "that was naughty" but didn't say anything because he'd have moaned I was criticizing his driving (he doth protest too much!). When I had a ranty phone call two weeks later because he'd had a fine I told him I'd seen him do it which bizarrely diffused his rage instantly as he realised he had nowhere to go with it.
Again, it seems a bit over the top to get a fine for going in it for a split second, or 5m, etc, but they have to (figuratively and literally) draw the line somewhere. Give people an inch and they'll take a mile, so they've got no option other than to be strict.
I would just be grateful it's a fine only and not points as well.