I found this fly in my back garden that looks like a beetle with wings and it hovers.
What is it?
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It is of course it is difficult to tell exactly from the quality of the image, but with mandibles of that size relative to the body (approx. 20-25% of total length) it is very likely to be a male Stag Beetle Lucanus cervus, the mandibles will grow much larger. The antenna sticking out from the side of the head just in front of the eye matches your photo (note: in the image below it looks like two on each side, but it is just the shadow in the photo)
Picture from Wikimedia commons https://commons.wikimedia.org/wiki/File:Lucanus_cervus_1922.png
They can be found flying at dusk, and are found in the SE of England from late May to August.
If you are looking for a good insect ID book, I can recommend "A comprehensive guide to Insects of Britain & Ireland" by Paul D. Brock, published in 2014