The council probably has a reason for not painting the centre white lines down the middle of the road. Because cars are always parked on one side of the road, a line down the middle would mean vehicles driving on the side without parked cars would probably not keep as left as they should, resulting in traffic coming the other way not having enough space to pass, so in my opinion the council has not painted the line in the hope drivers use common sense and leave enough space to pass each other.
I have attached an image of Rocks Lane in Barnes, Richmond upon Thames to demonstrate my point. You can see the old faded line was in the centre of the road but the council moved it because there are always cars parked on one side of the road. Now the white line gives traffic in both directions the same amount of space and traffic flows much better. Before the council did this, buses and large vehicles on the side with parked cars would often not fit through because vehicles travelling the other way didn't keep left, presumably because they felt they had a right to drive up to the white line.
Going back to the road featured in this report, I doubt the council could easily paint the line similar to the one I mentioned in Barnes because cars aren't parked all the way down the road, so the lines would have to wiggle which is far from ideal, hence why they may have felt no lines was the best solution.
This is in Exeter, I have driven down this road many times. There's always cars parked there, and I can vouch that two cars can easily pass each other on that section of the road (let alone a bike and a car), if they stay to the left. I'm guessing she didn't see you coming and just thought she could cut straight down the middle of the road. She was totally in the wrong.
Ducking into the gutter before parked cars is something you never want to do if you can help it. This is a particular problem on bicycles, as many (ignorant) drivers will see this as as green flag to over-take where they shouldn't. Stay away from the gutter and from car doors regardless of whether or not it puts you in the other lane. If people don't like that right then they can just sod off and re-take a driving test..
I hope this driver crashes because then it might knock some sense into the useless idiot