Your best (and only) option is to drive to Salerno, Italy. From there you catch a freighter-cruise from Salerno to Limassol in Cyprus (takes 7 days) which runs once a week. Goes via Pireas, Izmir and Alexandria.
Operated by Grimaldi Lines:
http://www.grimaldi-freightercruises.com/(Click on the Euro-Med Service link)
Of course you could skip driving to Salerno and just get on the freighter-cruise at Southampton where the ship starts its journey. Takes six days to sail to Salerno plus seven more to get to Limassol. A holiday in itself!