You cannot drive directly from the UK to Cyprus since both are islands. The distance between London, England and Nicosia, Cyprus is around 2000 miles (3218 km). According to the RAC route planner, it would take around 61 hours to drive from Essex to Limassol; this is the non-stop time. As its getting on for 3 days one would obviously need a few stops - so around 5 days in practise.
Cyprus is always two hours ahead of London. However, Northern Cyprus switched to Turkey Time (TRT), which is UTC+3 year-'round, on 30 Oct 2016. So the time difference between London and Northern Cyprus is two hours during British Summer Time (BST), from the last Sunday of March to the last Sunday of October, and three hours during the rest of the year.