It's funny, it's happened a couple of times lately.
The first time was at the junction as I leave work. It was a warm day, the driver's window was open, and it was probably somebody who works at my place (tho' I didn't know him).
As he was exactly alongside me, I looked at him, and when I'd caught his eye, asked him "so, which of us is going to go first?" He sheepishly replied "after you".
The second time was a different junction onto the same road. It really is busy - the crossing traffic is either doing 60 - 70 mph (despite all the SLOWs painted on the road at the approaches to junctions), or crawling at about 20 in a continuous stream one way and hammering by at 60 the other... You get the picture.
Anyway, this second guy pulled up to my left, windows tight shut, Radio 4 booming inside. No possibility of communication. When a gap came, he hesitated, so I went. When I was halfway across the main road, he lurched forward... and then found I was in the way. As there was no traffic coming, I completed the journey across the road slowly, watching him all the way. I may have mouthed "what are you doing?" (I certainly thought it!)
He ended up behind me when I reached the far side. I think the point was made.
The trouble with both of these junctions is that they are seriously dangerous. Cyclists have died at one of them and there have been numerous near-misses at the other. I'm not going to take any chances - if I make a mistake, I'll probably die. Unexpected behaviour by anyone at these junctions is not welcome - and is probably the cause of the accidents there have been.