The only sort of ongoing training which would probably be worthwhile is to re-pass the theory test every 5 years or so.
I still think some perspective is needed. The UK has a generally good standard of driving. I have been driving for about 20 years now and covered maybe 300,000 miles. In that time I can think of maybe three or four occasions where a driver could have caused me very serious harm had it not been for my alertness or fortune. And I have had one minor 5mph bump which was my fault. I have had one accident where another driver wrote off my car by rear ending me, but that was caused partly by the design of the road which induced a number of hazards following a light-controlled junction which was designed to "must get away quick off the mark".
Most bad driving is inconsiderate and annoying and can be managed by other road users' patience and forebearance and is not a problem which needs enormous change. What does need to happen is a change in behaviour among the 10% or so of drivers who drive recklessly or irresponsibly, and I don't think taking tests is of huge assistance.
Even hazard perception is only partially useful. In my view it's a vigilance test, where you click the button when you see a side road or a child walking near the back of a car. This only partly replicates the real world, where you are sitting physically in the car, feeling its performance and your envelope of risk changes substantially. A car waiting patiently at a roundabout as you go around it isn't a hazard in the perception test, but in the real world you will pick up on things you "don't like" from pattern recognition, subconsciously noting that perhaps you haven't seen the driver look at your car and that perhaps you haven't been seen (and will ease off the accelerator). Everyone gets that sixth sense feeling about vehicles "he looks lost and might stop suddenly" "this guy is a fool, I guarantee he will try to overtake on that bend". Those skills come from regular driving and not testing or competence training, and are skills which will keep you safe.
Britain needs better enforcement of traffic violations and more police on the roads, certainly. But I don't get the fixation on testing people; a person who has just passed their test is a risk and a liability on the roads because the test covers the minimum level of competence to operate a car.