It depends on which London airport you use, also Limassol doesn't have an airport - you have to fly to Paphos or Larnaca. It takes around 4.5 hours to fly from Stansted to Larnaca and then another 40 minutes to drive to Limassol.
6hr 45min to 7hr 15min London Gatwick (LGW) or London Heathrow (LHR) to Dubai (DXB) by a nonstop flight operated by British Airways, Emirates Airlines or Virgin Atlantic.