This is the Common Green Lacewing (Chrysoperla carnea). If you have these in your garden you are in good hands, as these insects will eat up your greenfly in great numbers. Note how fine and delicate the wings are, and the tiny hairs which help identify this species of Chrysopidae, which is a subfamily in the insect order of Neuroptera.
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Rear garden, Staffordshire, England. June 2017.