Answer: no one is ripping us off, except perhaps the state (in taxes).
The Telegraph complains that car insurance prices are up and this is due to frivolous legal costs. The no-win no-fee lawyers in some countries, like Britain, may have some impact. But the problem of raising insurance costs is visible also in countries that do not have no-win no-fee lawyers. There's another thing that people often don't appreciate nearly enough. It's the change in cars and their safety that we've seen over the last decades.
Modern cars are designed so that they contain the impact energy in accidents: the front of the car compresses in a controlled way, but the passenger cabin maintains form and protects people. The cars also have airbags - up to a dozen of them. And there are explosive cartridges that tighten the safety belt in an accidents. There are also many other features that help people survive crashes but which increase the manufacturing and repairing costs of cars. This is the main reason for having fewer people die in traffic accidents - the number of accidents is not going down so much, but the cars help people to survive more and more dramatic crashes.
This does have a cost. In the old times, your Mini or Opel Kadett C or Toyota Corolla could kill you if had a medium crash. Nowadays your Hyunday Getz, Opel Astra or Toyota Auris deforms itself, but you just walk away. But if you have a small crash - and there are many more of those than there are medium or big, fatal crashes - the car is totalled. Large parts of the fuselage need to be replaced, as well as the airbags, the parts of interior destroyed by the exploding airbag cartridge, etc. Often the car looks more or less intact on the outside, but it's written off, because it is so deformed that the doors won't close any more. It's not feasible to fix it any more.
If you have a small crash, but just big enough to launch the airbags, the car has to be recycled and replaced. This has a big cost for the insurance companies.
Look at the bright side: the injuries people get are diminishing. The cost to the health system is smaller. But car insurers pay this in cars that are written off, and that increases the insurance prices.