Driving a UK car to Greece. Is there a time limit to how long I can stay in Greece with this car?

You can stay as long as you want the UK and Greece were in the Europian union there was no time limit to how long you can stay., now that UK is out of the EU , not too sure but I think you can get an extended visa and stay for about a year.  

you can only stop for 90 days with a visa ..if you want to stay longer .ie become a resident ..its a very complicated and long process to register your car ..and you cant do it yourself ...must be done via embassy 

The status of British citizens in the EU is uncertain since Brexit was less than a week ago.  I recommend making contact with the office of your MP to ask for information. 

How would we know? Contact someone in Greece.