Build is not very well balanced. PSU is okay, but not reliable. Single Channel RAM is really not worth it. SSD is too expensive, and in that budget you can easily get a 1060 6 GB. I understand that a HDD in this build would be too tight in terms of space.
Motherboard is also overly expensive.
Cooler won't be required as the stock will do.
You are multitasking, a Ryzen 5 or 7 would be better. The 2nd gen is quite close to intel in terms of gaming as well. I have given both Intel and Ryzen builds.
You can build yourself for cheaper. Here:
Intel -
PCPartPicker part list:
https://uk.pcpartpicker.com/list/h98JMZ
Price breakdown by merchant: https://uk.pcpartpicker.com/list/h98JMZ/by_merchant/
CPU: Intel - Core i5-8400 2.8GHz 6-Core Processor (£143.99 @ Aria PC)
Motherboard: ASRock - Z370M-ITX/ac Mini ITX LGA1151 Motherboard (£118.96 @ Box Limited)
Memory: Patriot - Viper 4 16GB (2 x 8GB) DDR4-3000 Memory (£154.99 @ Amazon UK)
Storage: SanDisk - Ultra 3D 500GB 2.5" Solid State Drive (£99.96 @ Amazon UK)
Video Card: EVGA - GeForce GTX 1060 6GB 6GB GAMING Video Card (£262.76 @ Ebuyer)
Case: Cooler Master - Elite 130 Mini ITX Tower Case (£41.98 @ Amazon UK)
Power Supply: EVGA - SuperNOVA G2 650W 80+ Gold Certified Fully-Modular ATX Power Supply (£58.67 @ Amazon UK)
Operating System: Microsoft - Windows 10 Home OEM 64-bit (£79.99 @ AWD-IT)
Total: £961.30
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-05-09 13:36 BST+0100
Cheaper than 1000 Pounds. Faster and Dual Channel RAM. Better PSU. Cheaper SSD but also 500 GB. Better GPU.
Ryzen -
PCPartPicker part list:
https://uk.pcpartpicker.com/list/YbkXyX
Price breakdown by merchant: https://uk.pcpartpicker.com/list/YbkXyX/by_merchant/
CPU: AMD - Ryzen 5 2600 3.4GHz 6-Core Processor (£155.99 @ Aria PC)
Motherboard: Gigabyte - GA-AB350N-Gaming WIFI (rev. 1.0) Mini ITX AM4 Motherboard (£93.97 @ Amazon UK)
Memory: Patriot - Viper 4 16GB (2 x 8GB) DDR4-3000 Memory (£154.99 @ Amazon UK)
Storage: SanDisk - Ultra 3D 500GB 2.5" Solid State Drive (£99.96 @ Amazon UK)
Video Card: EVGA - GeForce GTX 1060 6GB 6GB GAMING Video Card (£262.76 @ Ebuyer)
Case: Cooler Master - Elite 130 Mini ITX Tower Case (£41.98 @ Amazon UK)
Power Supply: EVGA - SuperNOVA G2 650W 80+ Gold Certified Fully-Modular ATX Power Supply (£58.67 @ Amazon UK)
Operating System: Microsoft - Windows 10 Home OEM 64-bit (£79.99 @ AWD-IT)
Total: £948.31
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-05-09 13:38 BST+0100
Same system with Ryzen. Only problem is that the motherboard will require a BIOS update before the insertion of the new chip so you need to contact the manufacturer or AMD for the update.