In the United Kingdom there are three types of car insurance cover, although only comprehensive and third party fire and theft are usually available online.

Comprehensive Car Insurance Cover (Fully Comp)
'Comprehensive' covers the loss and or damage to the insured's vehicle, liability to third parties, and various other sections depending upon the type of car or vehicle involved. The term comprehensive is sometimes known as 'all risks' and describes a policy which brings together a number of different types of cover into a single policy document. For example a comprehensive car insurance policy will normally contain many sections including material damage, third party cover and may include a range of other extensions.
Under private car insurance some of the extensions to cover that are available in the UK are:
Personal Accident Cover
Rugs
Coats and Personal effects
Medical Expenses cover
Legal Expenses Cover
Audio Equipment Cover
Windscreen Cover

You should always check each company's definition of 'Comprehensive Car Insurance' in the policy wording, as many of the covers mentioned above will be additional costs if you purchase a 'limited comprehensive' policy which may appear cheaper but only covers damage to the car and liability for third party injury or property damage.

Third Party Fire & Theft Car Insurance (TPFT)
TPFT covers Third Party liability risks, that is damage to other people and their property, plus damage to the car if caused by either fire or theft .

TPFT covers loss or damage to the car resulting from fire or theft, and can be found within the 'loss or damage' section of a comprehensive policy wording. ( Otherwise known as 'Section 1' which is on an 'All Risks' basis)
The accidental damage excess under comprehensive policies which is often applied to 'young and inexperienced' drivers, does not apply to fire and theft claims.
An insured who chooses third party cover only, can usually extend this cover to include loss or damage to the car by fire or theft as named perils on the policy. This is what is meant by TPFT.
Loss or damage caused in other ways remains uninsured.

It is possible for an insured who has taken his car off the road for whatever reason, to insure the vehicle for Fire and Theft cover only, however you will probably need to talk directly to a Car Insurance Broker or company to obtain this cover, as we have yet to see it offered online over the Internet.

Third Party Only Car Insurance (TP)
This covers only the third party liabities as a minimum legal requirement for car insurance, in accordance with the compulsory insurance requirements of the Road Traffic Act of 1988. This type of cover is not usually offered online.

Whatever cover you opt for you should remember that you will only be covered in the event of a claim if you adhere to the cover you purchased. For example, if you declare when purchasing a policy that you will only use your car for social domestic and pleasure, and have an accident while using the car for business, your insurance will not cover you and the claim will not be paid.