I have written entire essays about this topic, haha.
It is anarchy in terms of which side, yep. If it's a busy street then usually if you're ambling and dipping in and out of shops, you'll be on the shop side, and if walking purposefully, on the road side, but if it's just a residential or other quiet street, there isn't a side preference.
There is a bit of an unwritten rule that whoever is going faster gives way to/works around whoever is going slower - don't try to get out of the way of a jogger or fast-strider, you'll only mess up their planned route based on your original trajectory. Similarly, individuals are assumed to nimbly work their way around couples or groups. More annoyingly, there's an assumption that smaller individual people give way to larger individual people, much as they do to slow people or groups, and this shades into women give way to men.
That slight dominance-game aspect does annoy me, and I sometimes make it a point to pretend not to be oblivious to what's expected of me. If I see a bloke coming towards me on the same side of the pavement, and he glances up, notes me, and immediately assumes it's MY job to get out of HIS way, I try not to. We play a game of chicken which I generally win at a point so late I have to really force myself to keep walking and not duck out of the way - but they do adjust course once they twig I'm not going to. Worst case scenario is to just stop, and let them walk around me. I've only had to do that maybe twice, although I've brushed shoulders countless times.
I want to hope the near miss makes people more likely to think 'oh, maybe it's a mutual responsibility to avoid a collision then', but probably all it does is make them think I'm an oblivious jerk. It's an interesting diversion anyway.
It's good manners for groups to leave enough space for people to pass them from behind as well as from in front, but it's rare, groups usually expand to fill the whole width of the pavement. If I'm walking with people I make it a point to go in front or behind once we reach critical mass. It's also completely natural to get annoyed if a group or person is blocking you from your natural stride and forcing you to shuffle-half-step. A few years ago I started just saying 'excuse me' to get past, works much better than tutting and hoping they notice, no one's reacted badly so far.