New 8th-gen Intel is right around the corner with hexa-core i5 and quad-core i3. Might even be a quad-core i3 with hyper-threading. Maybe wait until we see more. Other than that, Ryzen 5 1600 would be a great option, just have to fit a few more pounds in your budget for a decent motherboard, here's one for kinda cheap. PCPartPicker part list
/ Price breakdown by merchantCPU: AMD - Ryzen 5 1600 3.2GHz 6-Core Processor
(£184.95 @ Amazon UK) Motherboard: MSI - B350M BAZOOKA Micro ATX AM4 Motherboard
(£71.64 @ Box Limited) Total:
£256.59Prices include shipping, taxes, and discounts when availableGenerated by PCPartPicker 2017-08-22 23:58 BST+0100
But again, maybe wait until we see more from Intel. Though I actually like the idea of AMD's Ryzen on AM4. Longer support for AM4 socket than Intel will ever give one of their sockets.