The opposite corner has curb cuts which have eliminated parking there.

Urban compact modern roundabouts start out at around 90 feet in diameter to the outside curb. Mini-roundabouts are usually capable of fitting inside a 60-ft diameter space, but mini-roundabout islands are mountable for large trucks (no signs on the central island). 23rd looks like a typical width, while Anza looks closer to 40 or 44 ft wide. If the intent was a mini or ultra-compact urban modern roundabout, then standard practice would be to include splitter islands on each approach, crosswalks set 20 ft back from the yield line and comensurate parking removal to clear the visibility.
The key to a modern roundabout’s safety is the slow operation. 15-20 mph is the appropriate operational speed. This is only achieved by deflection – requiring motorists to go around something and slowing to do so. Smaller circles have less deflection and less slowing (conversly, very large circles also have higher speeds). For neighborhood traffic circles the idea is to provide a minimum lane for auto traffic, about 13 ft around the circle, clearly mark the crossings to keep ped and auto paths from overlapping, and make the circle as large as will fit within those constraints. A narrow truck apron is provided to let longer vehicles travel through intersections, though not necessarily make left turns.
I would also point out that the liability laws in the UK are quite different than the US, and the rights of pedestrians significantly greater.

Circular intersections change the number of conflict points possible. the only place motorists can run into each other at a circular intersection is where one car enters while another is circulating. The reduction in speed (typically 15-20 mph) also significantly decreases the likelihood of serious injury if a collision does occur, first because at 20 mph you have more time to react and second, due to the reduction in energy. The geometry of crashes at circular intersections is also a factor in the reduction in injuries (glancing sideswipes instead of 90-degree angles). Neighborhood traffic circles are objects in the road that must be driven around. Impaired motorists will run into them – one nickname for these small neighborhood circles is DUII-catcher.
BTW, the City has confirmed that existing traffic control will remain in place – this is the normal way for small neighborhood traffic circles like this.