Anecdata:

We recently instituted a 20mph limit across our town (I’m the chair of the town council and also a keen cyclist). We do regular speed surveys.

Not everyone sticks to 20mph. But no one drives above 30mph any more. When we had a 30mph limit, we’d regularly get people driving up to 40mph.

So it’s not perfect, but it does make a difference, here at least.

My city has done quite a good job of making itself much more cyclist friendly over the last couple of years and reducing the speed people drive. Most of the roads were already more than wide enough before for bike lanes, but that came at the expense of people driving at 60km/h in densely packed urban areas (the speed limit is 40, but nobody cares).

- On quieter roads in retail areas they added painted white lines, but most importantly they've enforced them so delivery drivers don't park over the cycle lane.

- On roads in busier areas that had street parking they've shifted the street parking inwards a couple of meters, and put a cycle lane between the street parking and pavement. This means the driving part of the road is narrower, so people drive slower.

- On other streets that were too small for a cycle lane and street parking, they have removed street parking and put up a cycle lane separated with small bollards (a few cm high, so can be driven over). These are usually in areas where you would have only driven at 20km/h. We have a lot of cobbled streets and they aren't (I'm wondering if it's intentional) very well maintained, so most are very uneven. The only issue with these is that delivery drivers do park over them, because now there is nowhere else for them to park. Of course people complained about the reduction in street parking, but that issue was quickly forgotten.

- They changed a lot of road directions (bikes are exempt) so that you cannot drive through the city center to get across the city. This did increase traffic a little in other routes (this happened at the start of this year, so hard to tell because of covid), but it means that as a cyclist you can easily cycle through the city center which has much less car traffic. Of course people complained, but again it was quickly forgotten.

- A few streets that were popular for commuters were tested being pedestrian only in the summer (case numbers here were fairly low then, so traffic levels were maybe 75% of normal). Again people complained, but the issues were quickly forgotten.

- Proliferation of food delivery services have meant there are much more bikes on the road, so drivers are more cautious.

I live in a city that dropped speeds from 30 to 20. The change didn't happen overnight, but the average speed has dropped from >30 to >20, which is a world of difference

My understanding is that narrower lane widths do cause drivers to slow down. The signage stating a 20 mph limit may be ignored, but if all the other lane lines get repainted narrower when a bike lane is put in, then cars will drive less aggressively.