The default speed limit in built-up areas should be lowered to 20mph. There's plenty of evidence that this does change actual speeds, even without increased enforcement, and does reduce injuries and fatalities.
This limit can be raised to 30mph on stretches of road where that is appropriate, after a safety audit. This should require good visibility, sufficiently frequent crossing places for pedestrians, adequate (LTN 1/20 compliant) cycling infrastructure, and the absence of schools, parks, care homes or other destinations with large numbers of vulnerable users.
The default rural speed limit should be lowered to 40mph and only raised to 50mph on stretches that have been given a similar safety audit. Are there adequate footpaths and separate cycle tracks? Are there safe crossing places? Is there clear visibility on all approaches?
Local authorities should be allowed to set 10mph speed limits in short stretches of streets: outside schools and care homes, for loading/service traffic to otherwise demotorised city centres, and in other areas with high concentrations of walking and cycling and vulnerable people and relatively low motor traffic volumes.
Road danger is not so significant an issue on motorways, where there are no vulnerable users. But here the long-distances travelled make reducing carbon emissions a more pressing concern. Given the climate emergency, the motorway speed limit should be lowered to 50mph, which would minimise emissions for most cars. To encourage modal shift, buses and coaches could be allowed to do 60mph and given exclusive use of the outside lane.
Then we need to actually enforce speed limits, and develop a culture where speeding is as socially acceptable as drink driving.