It is perfectly possible to insure most imported cars for UK roads, but firstly you need to know what type of import your car is.
There are two types; there are so-called 'parallel imports' and 'grey imports'.
These are cars which have been built within the European Union. This means that they have been built to specifications which are acceptable to the UK. In many cases these are available within the UK from main dealers in right-hand drive format, whereas the imported one is more likely to be left-hand drive. This means that the majority of spare parts will be readily available over here in the event that they are needed following an accident. As a result repairs can usually be completed quickly and reasonably economically.
Insuring a recent model parallel import car should be reasonably easy, although it may cost a little more than insuring the equivalent home built one.
These however have come from outside the European Union. Those from Japan are usually right-hand drive, whilst the Americans send left-hand drive models.
Unfortunately it is unlikely that these will have been built to the same safety and emission specifications that exist in Europe. Before they could legally be driven on British roads they would possibly need extensive modification before they could comply with these standards.
The reason why they are imported is usually because they are high-powered and very sporty machines. They are usually bought by enthusiasts, who may be more likely to drive them hard. This by itself makes them a bigger risk for the insurers.
In addition, spares may be very difficult to obtain. This pushes up costs for insurers since in the event of an accident it may be necessary to import new parts, which not only costs more than buying from a local stockists but also causes delay in getting the cars repaired.
An insurer will want to see all the necessary documentation to confirm that the car is in compliance with UK standards. They are also unlikely to have very much statistical information about the chances of them being involved in accidents, and what those accidents are likely to cost them. This pushes up expenses for them at a time when most of them prefer to concentrate on automated systems for getting quotes and issuing policies, such as price comparison engines. As a result it is usually necessary to discuss the matter with a specialist broker, who will know which insurers to approach, and can help with all the necessary formalities.