I have done a quick "street view" and just a short way back from each arm of the roundabout, it is a single lane.
The 2-lane in and out is trying to maintain the existing capacity of the roundabout, but in terms of through-put to the junction, it really is a small element which is actually wiped out by the prescence of 4 zebras (which are very difficult to model). The only issue would be with one arm backing up ont the roundabout, all traffic would have to stop, but as this is in Central London, I am not sure this area runs that freely in the peak anyway.
Having the 2 lanes on the roundabout itself allow traffic heading north-south or east-west to "take the racing line" under free=flow conditions and so create a safety risk for all other users (including other motorists).
2-lane approaches to zebra crossings can also be dangerous for pedestrians if one lane is slow/ stationary and one is clear as pedestrians are masked by the slower lane (I know this is an existing layout).
From what I can work out, the proposal is simply 4 x speed tables (which is good from a speed-control perspective) and the hatched area kerbed. I know they are also suggesting shared cycle-tracks as well, but this is a cop out given so much space. TfL claim that it is lawful to cycle on zebras (because it is the carriageway and cyclists can use the carriageway), but cyclists have no priority over traffic when crossing (in the same way as pedestrians do).
A radical solution would be to ditch the 2-lane approaches and use raised and segregated cycle tracks which can be given priority over traffic where they cross - it would be very unusual on such a busy route, but it is legally possible and with a blue CS track it would be pretty clear and if cycle numbers are relatively high, it should make sense.
The loss of the traffic lane would then allow a compact roundabout to be provided which would operate more slowly, but more predictably for all.
I really don't think we should be designing for worse-case peak traffic flow any more, it hasn't worked and left us with historic layouts like this.