It is not my premium being the issue, mine is dirt cheap as I pay £850 for 4 cars. Does not mean that I can not get frustrated about the injustice of it all though.
Principle is so simple (simplified example):
Europe:
Annual payout by insurance company: 1 million
1 million drivers, each paying £1 premium.
Now add the bonus malus system:
Everyone starts at 140% as a new driver of the standard premium of £1. Ignore for now the experience / no claim, type of car etc lets just concentrate on the third party element.
After 1 year no claim, premium goes to 120%, then after another year to 100%, then to 80 etc to the maximum no claim of 75%, i.e. paying 25%. Therefore, experienced drivers pay less, not experienced more. All simple so far.
Now get a claim, you drop 20% each time, so the accident people pay for the higher premiums.
There is a fund, like in the UK, for uninsured drivers. It is small however, as the premiums are all reasonable so 99% pay the premium.
As the car is insured, it is up the the insured person to let someone else drive. They crash, your premium goes up by 20%. End of story, everyone knows the score and you never have an uninsured car because the driver does not have insurance.
If there is a non fault accident, nothing happens to your premium as your company has not suffered a loss. All fair, the guilty party's insurance goes up and pays up. As everyone pays premium, the uninsured premium contribution is say 1% of your total premium.
Now take the UK:
Experienced drivers pay roughly the same as the European counterparts for the base premium. New drivers pay 1000% premium hike compared to other drivers, so they are priced out of the market and don't bother buying insurance as the fine is next to nothing.
This means that the uninsured fund has to be huge, therefore all other drivers have to pay a large contribution to this fund. Premium goes up again for everyone.
Now there is a claim from driver A (innocent) against driver B (guilty). Driver B pays more premium as his company paid the liability. However, now the weird bits come in. Driver A's premium also goes up based without foundation. This is unjust.
Also unjust are the premium increases for traffic penalty points, modifications that have no bearing on the risk.
As said, none of this affects me ...