If your car has numberplates beginning with the letter Q then you will almost certainly be turned down automatically for car insurance if you try to order it online.
Essentially; it is a numberplate for a car whose full identity is not known. A car is normally issued with a plate when it is first registered, and this stays with it, unless it is change for a personalised one (details of which are recorded by the DVLA), until it is finally scrapped. This means that the vehicle can be identified positively at any time.
Sometimes however cars come from sources which cannot be positively identified. Some of these are military vehicles, the origins of which are protected under security regulations; some are imported; sometimes they are kit cars which have been rebuilt in order to look like more popular models, such as famous sports cars; and sometimes they are vehicles which simply cannot be identified because they do not have a vehicle identification number (VIN).
The problem with these vehicles is that it may be extremely difficult to confirm that the car meets all the necessary rules and regulations regarding safety and emissions. Plus of course, from an insurance company's point of view, it is impossible for them to slot it into one of their statistical categories that they base their premiums on.
To be allowed on British roads, and to be given the Q plate, the car must first of all have a Type Approval. You can get more information about this, including how to go about getting one, at this UK government website.
Getting a type approval can only be done if the vehicle has a Vehicle Identification Number; this can be provided by the DVLA if necessary. It is then inspected to ensure that it meets all relevant EU safety and emission standards. Plans must also be submitted to show every stage of the building process.
This process can be reasonably straightforward if a conversion kit has been supplied by an approved manufacturer; but it can get more complex if different parts have been used from different sources.
Provided that the car passes this stage the next difficulty is to find an insurer. The vast majority of insurance companies will not even consider one of these cars; it will be necessary to find a specialist insurer. This company will need to be satisfied that the vehicle is indeed safe and so a lot more information about it will be required than is normal.
All of this cost money. Insuring a Q car can be a difficult and frustrating exercise which is best left to a competent broker.