The Good Housekeeping Institute recommends the following as the correct order in which to wash up kitchen items (after clearing envelopes/keys/food away):

• Scrape off as much food debris as you can. Give each dish a quick rinse before stacking at the side of the sink ready for washing.
• Soak by filling really grimey items such as pans with hot water and put them to one side to soak. 
• Clear up by making sure your sink is clean before you start. Using a plastic washing up bowl uses less water and helps to protect items from the sink's hard surfaces. If you don't have a double sink, the gap between the bowl and the sink means you can still use the hot tap for rinsing.
• Glasses
• Mugs & Cups
• Saucers & Side plates
• Dinner plates and Bowls
• Cutlery
• Serving dishes
• Pans
• Roasting tins

Then:

• Spray and scrub worktops
• Clean crumbs/oil and wipe over oven hobs
• Wipe down small appliances (including the inside of the microwave)
• Sweep floors
• Empty bins