Context for our American friends. This isn't specific to London. Everywhere I've lived in Europe is more roundabout-heavy than the USA. Because, you know, they're objectively superior ;-)
They are also spreading in the USA. New Jersey has had them for quite a long time, and is building more. I've been surprised to see them as an apparent new default for new intersections in central Wisconsin where my wife's family is from. There are even some new ones being added around Santa Fe where I live.
The ones I've seen are really more of a half-hearted traffic-calming measure than proper roundabouts. The intersections I can think of, they're in residential neighborhoods and there's just some new island in the middle of a four-way stop. It might be impossible to widen these into proper roundabouts due to the houses up to the property lines?
Placing new STOP signs in the UK required written permission from the secretary of state until some years ago. They're still quite uncommon here, typically reserved for more risky junctions.
We most commonly use the "Give Way" sign at junctions instead, indicating that other traffic has priority.
*Given that the roundabout is fed by single-lane streets with low traffic and excellent visibility and no stop signs before entry, which would otherwise negate the advantage of quicker entry.
Single-lane roundabouts aren't very uncommon in America. Maybe not as common as in the UK, but they're definitely around and virtually every driver in America should be familiar with them. There will always be a few fools who don't grok them, but the same can be said for any aspect of driving.
I think when Americans say they're baffled by UK roundabouts, they're almost always talking about the huge multi-lane roundabouts. Those, to me, are nightmare fuel.
My French relatives are always impressed with the (mostly) civil behavior at 4 way stop signs in California and claim they would never work in France. It’s funny to me because every time they visit, they comment on them.
I left France too young to know if they are right though.
I think what your relatives mean is that if everyone has a stop then it'll be messy because everyone will try to go first after they have stopped...
Here in the UK they have installed 2 stops and 2 give ways at a nearby crossing and it's already quite dangerous because no-one is sure what to do: those with give-ways think they should go before those with stops, those with stops think they should go first if they arrived first... honking ensues very often. If you're lucky it ends in a very British "you go first, no you go first" contest, which is not very practical, either.
That sounds dangerous. It’s not uncommon for different people to order events differently, I can see two cars crossing at the same time, each driver convinced to be first.
It does lead to quite a few 'what the f.. arms up.. stares' when there is a perceived violation but it works. Probably because the cars within the stop signs are going relatively slow.
given that people generally don't spin their tires off the line from a stop sign, it's fairly safe. If it's obvious that two people are going at the same time then one that has advanced less far in that time will generally ease off the throttle and let the more advanced party continue.
there are accidents, of course, but i'm not sure of any 4 way traffic junction that's infallible.
and as others stated, right-of-way rules are observed atop the social norms.
Specification unclear. If two or more entries to the intersection have at stopped vehicle waiting to cross, a waiting vehicle is somewhere "on the right" of each waiting vehicle. If only two vehicles are present, and are across from each other, and at least one of them wants to turn across the path of the other, each vehicle is _equally_ "on the right". A relative reference is not sufficient.
Some people try clock-relative turns, but that only works if the vehicles arrived while an existing rotation (of prior vehicles) was in progress.
I think most people obey 4-way stop-sign intersections because they're afraid of getting T-boned by another car, not because they obey signs for the sake of obeying signs. People ignore signs when they can get away with it, but a 4-way stop-sign intersection is not such a case to anybody but the suicidally reckless.
The ~dozen or so roundabouts near where I live (northern suburb of Atlanta, Georgia) have all been 4-way stop retrofits. And all in the last 10 years or so.