If you do a websearch in importing car from UK to Cyprus you can get lots of info.
'There are a number of agencies who can make the transport arrangements both based in Cyprus and the UK - Transport Costs depend on the size of the vehicle. I have seen internet quoted shipping prices starting at GBP 320 + VAT for a small saloon, using a Ro-Ro , most quotes are in the GBP 460 area. That is from port to port. You need to arrange to get the car to the agents. many can collect but you pay for the distance from the collection point to their depot or arrange delivery to loading port in the UK. Then there are arrival fees at Cyprus, with quotes starting at GBP 385.
The car needs to be registered with the department of transport. I understand that costs Eu 150.
You will need a vehicle inspection (MOT) cert, the old plates and UK registration documents
Then you have to pay excise duties.
if you look here you can find the details of excise duties
http://www.mof.gov.cy/mof/Customs/customs.nsf/All/505369EB35BEDE8B422579040055CC92?OpenDocumentThe bigger CO2 producers pay more.
good luck