He blows the case in the the answer to the very first question.
"Surely what you are suggesting is undertaking?"
Now in this thread it has been pointed out how stupidly dangerous it is to overtake turning vehicles - this seems to be be universally accepted when the example involves a car overtaking a cyclist, and why the Highway Code tells us not to do it on the approach to a junction. But the apologists for the petition have tried to deny this is what the petition is about at all and somehow undertaking is different - and that quoting the actual words of the petition is somehow misrepresenting it.
Boardman makes it abundantly clear that in his view that cycling on the left is the natural place to be so overtaking on that side is legitimate. Fair enough - we do permit overtaking on the left past queuing traffic - but it is still overtaking. So should be treated with the same rules of priority as normal overtaking on the right. Indeed, because the normal rule is to overtake on the right you need to take greater care when overtaking on the wrong side.
And that is before he gets to cycle lanes. When he says "We need to start thinking of cycle lanes as a legitimate lane of traffic" he is quite right. A traffic engineer would never put a lane for left turning traffic to the right of a lane for left turning traffic. You would never ever ever see markings such as this: http://www.warringtoncyclecampaign.co.uk/facility-of-the-month/August2001.htm
for legitimate traffic lanes., but he uses the stupidity of the lane markings to argue for changing the rules - rather than to remove the dangerous lane markings. He brings up the case of bus lanes, but bus lanes are interrupted on the approach to junctions so that turning traffic can merge into the lane on the approach to a junction, rather than be forced to swerve across at the last minute.
So on to the second question:
"Why would I trust a car to wait for me, isn't it better not to take the risk?"
To which he answers "He wouldn't" - quite b***y right. case holed below the waterline.
It is not the rules that make overtaking turning traffic dangerous - the rules are there because of how dangerous it is. It is not about whether you are driving a bus or a car or a bicycle - or whether you are overtaking on the right or the left. It is that when we are driving or cycling we are facing forwards and paying most attention to what is in our natural field of view. The driver or cyclist coming from behind has a much better view of the emerging situation which is why the highway code makes overtaking the responsibility of the overtaker rather than the overtakee.
Then we come to the "big benefits for drivers that this campaign hopes to unlock". Here hes is talking about removing pedestrian stages at traffic lights or the motoring organisations put it "dead time when no ones crossing" No wonder he can boast of the support from the RAC & AA for the proposed changes.