Car Insurance is a legal requirement to drive on public roads in the UK
The most basic level of protection is third party insurance which only covers costs for compensating others for loss or injury caused by you. Third party fire and theft insurance (TPFT insurance) will in addition provide you compensation if your car is stolen or damaged by fire (which is quite limited when you consider all the ways a car could be damaged!). Neither Third Party or Third Party Fire and Theft insurance will cover your own costs if you are involved in an accident where, if it is not your own fault, you will need to attempt to claim from the person causing the accident.
Comprehensive car insurance provides third party fire and theft and in addition would normally cover damaged caused to your vehicle by reasons other than just fire. Many insurance companies offer additional benefits such as a replacement car while yours is off the road, legal cover to help with recovering losses which are not covered by insurance.
Most insurance companies will offer a discount for a year or more of cover where no claims have been made (by yourself or others). This should not tie you to an existing company as all insurers will ask for details of claims history and traffic convictions (however this is one time where points don´t equal prizes and could lead to serious additional premiums or other restrictions). It is vital that you always disclose these facts and any thing else that may affect the premium (such as where the car is kept, changes to its standard original specification) as this may allow the insurer to withdraw cover when you claim.
The UK police use ANPR (Automatic Number Plate Recognition) to check if your car is insured. Check your insurance is registered on the police ANPR (external link).