On the advice of a friend, I took my car to the "Best" car wash in Larnaca, the one diagonally opposite Carrefoure (used to be Chris Cash and Carry).
My car was filthy (much to my shame) both inside and out, but after 30 minutes it was returned to me looking like it had just come out of the showroom! It was immaculate, and great effort had been applied by the staff who succeeded in removing dog hairs etc. The carpets all came out and were cleaned, and the windows have never been that clean either! Even my tyres had been washed and polished! And all of this for a mere £6cy.
I'm not normally given to making commercial recommendations, but if you can't be bothered cleaning your car yourself, you probably won't find anywhere better!