In such circumstances, ahead of you and snaking away to your right is a (usually stationary and long) line of vehicles queuing up for the on-ramp. It is your task to get through this line without blocking traffic, getting side-swiped or being sworn at by other motorists. It's not easy but this is how it is done.
First, you must wait until the roundabout is clear of vehicles approaching from your right. Then you must identify there is sufficient space between the traffic island at the top of Greenlane West and the queue of vehicles for your car to rest while plotting Part B of this manoeuvre. (If there's not enough room, your vehicle could block a lane. I've not made this mistake but if you do there will be honking.)
Then you must go! Forward! Now! Then stop where it is safe. Once you've reached the little waiting space, it's time to execute Phase Two. It is likely that the vehicles to your right are still stationary as the drivers are waiting to access the choked northbound on-ramp. It is almost guaranteed there's space ahead of them which will allow you to pass in front. (These motorists are politely not blocking the path of vehicles approaching from Greenlane West.)
At this point, multi-tasking is required. Obviously your right indicator is already on. You must look left to check that the motorists approaching from Greenlane West have not interpreted your lack of motion for a willingness to wait for them to proceed through the roundabout. You must look right and slightly behind you to check that the queuing motorist you are planning to move in front of has identified your intention to cross its path. You also hope this driver views you as a neutral player in this game. You are not trying to skip ahead. You are simply trying to get through this line of traffic.
Then you must go! Forward and towards the right! Now! Remember to wave your right hand to thank the driver in the queue who has taken the trouble to not T-bone you. Take a deep breath. You just survived a very tricky little vehicular dance. Congratulations!
As the correspondent from 2012 pointed out: "Should a driver simply wait until the roundabout is clear before proceeding, in accordance with the Road Code, then it is likely that his clothes will have gone out of fashion before he completes this move." Quite.
It definitely defies a few well-established principles of driving so I was reassured when a police car did the same thing. But, some unscrupulous motorists harness this situation for their own benefit. Just the other day I saw a driver in my rear-vision mirror attempting what I thought was the same manoeuvre as me. In fact, this person had entered the roundabout earlier, passed all the vehicles queueing for the on-ramp, then placed himself (or herself) at the front of the line for the on-ramp. That's not nice.
It reminds me of those drivers who fail to queue in the correct lane in Alpers Avenue, Newmarket, in anticipation of accessing the Gillies Road on-ramp. These people get swiftly through the traffic lights, turn right and then think the cars in the left-hand lane are going to let them in. Who are these people kidding? Of course, some drivers do take pity on them which just encourages such selfish behaviour.
One final comment about the complicated scenario at the Greenlane interchange: I'd pay money to watch driverless cars try to get through this roundabout. It'll be guaranteed chaos. Popcorn, anyone?