Dedicated and separated cycle lanes are the way to go. Cars, cycles, and pedestrians all need their own space. The challenge for the UK is our often quite narrow existing roads. Making space for physically separated cycle lanes is often going to mean taking lanes away from cars. Which is not necessarily a bad thing but obviously creates a lot more friction to be implemented.
Many cities in Europe have had an easier time with this due to more post-war modernisation/rebuilding that created wider roads.
Reducing suicide is always approached as trying to block pathways to death, rather than by improving life.
As always with this country it’s putting a plaster over the symptoms rather than addressing the cause.