The first one on our list is the junction at Balham Station.
The approach to the junction has all sorts of hazards.
Above: More parking bays. If you look carefully, there's a vehicle about to emerge from the filling station, and the driver's view of the cyclist is obscured by the parked car. It's an accident waiting to happen.
You'll notice in none of these pictures is there enough motor traffic to occupy the two northbound lanes, even though this is rush hour. Take note, people who think there isn't enough space on London roads for segregated cycle paths. Note also that TfL won't be reviewing the hazards you can see above, because these are minor junctions that don't count.
Now onto the junction itself.
The approach, above, is in a bus lane, which is wide enough to permit overtaking at the bus stop.
Above: A car in the advance stop-box.
You can see that so far there's been no attempt whatever to improve this junction for cycling. Really the minimum that needs to be done is to have a proper approach lane in both directions. An advance green phase would allow cyclists to get away in advance of the general traffic. On the exit to the junction, in both directions there is space to have a mandatory lane. The cycle lane should continue through the junction, and there needs to be some attempt to prevent 'left hooks'. During the green phase, there are particular dangers from the high vehicle speeds that arise from the motorway-style road layout to the south of the junction; this needs to be addressed.
One innovative possibility that takes advantage of the existing 4-way pedestrian green phase is to allow cyclists to wait in a reservoir in front of the pedestrian crossing, rather than behind it. They could then proceed carefully through the centre of the junction during the 4-way pedestrian green phase, and wait behind the crossing on the far side until the lights change. That arrangement would give cyclists a considerable head start on motor traffic. Or even more radically (make sure you're sitting down now), the 4-way pedestrian green phase could simply allow cyclists to proceed at will, with pedestrian priority, turning the junction temporarily into a shared space.
Of course, with TfL in charge of the redesign, we should be careful to lower our expectations appropriately.