Let's examine this example a bit closer.
If the speed limit was 20mph, and we assume that there would be no reduction in delays at the junction - which will be shown to not be the case - then at 20mph, the journey time will increase from 30 minutes to 33 minutes. Given the variation in journey times from day to day, this increase will be unnoticeable.
At worst, with the delay of rush hour or without it, the increase in journey time is a few minutes, which is about the same amount of time that would be spent around the water-cooler discussing last night's football match.
Figure 1 shows just how little extra journey time a 20mph speed limit would - even before reductions in junction delays.
Figure 1: Total journey time by speed limit
The same idea applies to signalised junctions. When traffic lights break down the car drivers need to slow down and negotiate the traffic lights. The rule of 'right-of-way' no longer applies, and instead the car drivers need to negotiate and co-operate. Instead of spending time moronically staring at a red light, the car driver is always moving. This idea has it's fullest expression in Drachten. The removal of the concept of 'right-of-way' slows the traffic down - the road users need to work together - but the junctions work better, and the junctions are also safer. The end result is that car drivers get where they are going faster. Essentially, the 80% of the journey time accounted for by the junctions is being reduced - the effort is being applied where it counts the most, instead of reducing the 20% of journey time by allowing drivers to take 'right-of-way'.
The crucial point is that the cars have to slow down to around 20mph for the co-operation to take place - car drivers cannot react quickly enough at 30mph. This is why a 30mph speed limit leads innevitably to 'right-of-way' operation, with the car driver looking well down the road, and not being a position to co-operate properly with car drivers around them.
The reason why a lower speed limit is safer can be seen in Figure 2. As the speed decreases, the stopping distance also decreases, meaning that it is more likely that the car driver will be able to stop in time or at least hit the obstacle at a much reduced impact speed. Also, because at 20mph, the car driver has more time to take in their surroundings it is much less likely that the collision will happen in the first place.
Figure 2: Typical stopping distances by initial speed (Source: Highway Code)
The best way of enforcing a 20mph speed limit is by fitting speed limiters to the cars. It obviates the need for speed cameras (unpopular with the public) and traffic calming (speed humps are marginally effective for larger cars). The technology exists to do this already - and by starting with a pilot town or city, and providing speed limiters to car drivers to use, the technology can be perfected. A country-wide roll out would follow the inclusion of speed limiters as standard in new cars, and if necessary the retrofitting of the device to nearly-new cars.
Sometimes, it is suggested that the faster a vehicle travels, the quicker it is past a point of danger, and therefore the shorter the duration in which an accident could occur. This is a myth. The risk is the likelihood of the accident multiplied by the magnitude of the danger. If we assume that the point of danger is located in any one spot, then the reduction of duration is counterbalanced by the increased potential speed of impact. The very act of trying to get past that location as quickly as possible guarantees that the vehicle will be going quickly, possibly accelerating, and certainly not braking. The point of danger is usually not located in one spot - as an example, a school may be in one place, but the children walking and cycling to the school will be located in many streets around it. Then there is no benefit in getting past the point of danger, since there isn't one. All that driving faster will do is to position the vehicle elsewhere a bit faster.
Recent research has demonstrated that young children have difficulty with judging the position of approaching vehicles where the speed limit is above 20mph. So, that's another good reason to restrict the speed of vehicles to 20mph.

Figure 3: CO2 emissions by speed - Source: Highways Agency
The first thing to notice is that the original title of the graph is missing - this is typical. The same graph is available on the DfT website. Here the graph is shown with its original title, indicating that the graph is for a Euro II diesel car. However, Euro II dates from 1993, and the next standard, Euro V, is due in 2009. Thus the graph is not even indicative of modern cars, let along future designs.
Next, it should be noted that the graph cannot be interpreted in the way that some people wish it to be. As the text alongside the graph makes clear, the graph also takes into acceleration and deceleration. So the graph includes, at lower speeds, the effects of congestion in the urban environment, and the stop-start nature of driving in towns and cities. A fairer comparison was done by What Car magazine, demonstrating that fuel consumption rises with speed, as would be expected.
In other words, fuel consumption will actually go down with a reduction in speed limit from 30 mph to 20mph.
Further, there are two additional effects, which are usually forgotten. Firstly, with 20mph speed limits, there will be an increase in cycling and walking, both of which are CO2-free. Secondly, downward pressure can be put on the size of vehicles used and hence their emissions, and this is anticipated with the next iteration of the Euro standard. Put together, the net result is a reduction in CO2 emissions, not an increase, even with the introduction of a 20mph urban speed limit.
The capacity of a lane of traffic was modelled. It was assumed that traffic proceeds with a 2-second interval between each car, and that the length of each car is 4.0m. The capacity of the road is then simply the speed of the vehicles multiplied by the vehicle density (mph and vehs/mile, or km/hr and vehs/km). The result is shown in Figure 4.

Figure 4: Capacity of a traffic lane by speed
At zero speed, the capacity is zero. This is because the vehicles are 4.0m long, and therefore cannot be reduce below a given density of about 400 cars per mile. As the speed rises, the vehicles are spaced out futher apart along the road, and so the length of each car becomes less important.
The difference in capacity between a 20mph road and 30mph road is only about 5%. The capacity of a lane of road will still exceed that of a lane at a junction, and so the difference in capacity at different speeds is irrelevant.
Moreover, along the roads and at the junctions, the increase in cycling will reduce the traffic flow. Traffic flow is measured in PCUs, where one PCU is the equivalent of one car. The number of PCUs that each form of transport typically takes up per person is shown in Table 1. Clearly, a significant increase in cycling will reduce congestion at the junctions, reducing the delay here.

Table 1: PCU value for various forms of transport
Please note: if the speed limit chosen was 15mph, to accomodate slower bicycles (like folding bicycles), then:
On a co-operative transport system - many people today bemoan the loss of a polite society, where people help each other out. The author thinks that this has much to do with the transport system, where you only get a parking space and space on the road if you fight for it. The notion of 'right-of-way' means that car drivers get annoyed when another car driver intrudes on their road space. A 20mph speed limit enables co-operative motoring, which is a nicer way of doing it. It is impossible, surely, to separate a violent society from it's competitive roots, of which transport appears to be a large component.