Absolutely, you will be hard pressed to find people who don't think that car insurance in the UK needs reforming. Even insurance companies are pushing for reforms such as the banning of referral fees; the only reason they accept them is that if they don't then someone else will. They also want to see rules for injury claims tightened up as it is very easy for someone to put in a false injury claim and very expensive for insurers to contest it so they are forced to just roll over and pay out a huge number of fraudulent claims. Given that there is an entire industry devoted to encourage insurance fraud it shouldn't come as a surprise that premiums are high. It isn't as though insurers are making much money out of it: for every £1 they take in premiums, they pay out £1.20, car insurance is being propped up by other forms of insurance. The trouble is that too many people see car crashes as easy money, from the claimant who pretends to have whiplash to the ambulance chasers taking huge fees for very little work or the garage doing unnecessary work for inflated costs to the claims management firms who buy lists of details and cold call people to get them to claim. Until such time as we stop the merry-go-round of leeches who bleed the insurance industry dry, premiums will continue to rise.
WRT common law right to travel, it is just that. A right to travel. It doesn't give you the right to drive on the road network, it is just the right to travel throughout the country. Common law also states that your liberties are subject to respect of the rights and liberties of others, without car insurance you cannot meet the rights of compensation to other citizens if you are involved in an accident with them, so driving without insurance is a breach of common law anyway. It has been tried time and again and every time the judiciary, who are the legal experts, have ruled against it.