I would not recommend pairing a i7 with a 1050ti. The GPU has the biggest impact on framerate for gaming and you will be putting too much money into the CPU and not enough into the GPU. With that being said, the i5-8400 is a 6 core CPU that is just as good as the 7th generation i7s.
You probably don't need 16gb of RAM either, because on the majority of games, you would have better framerates with a 1060 6gb and 8gb of ram instead of a 1050ti and 16gb of RAM.
I would go with something like the parts below and consider selling your 1050ti and getting a 1060 6gb or 580 8gb (they have a similar price). This build is 150 under your budget and after you sold the 1050ti you would be real close to a 1060/580. Or you could get this system and run with your 1050ti for awhile and upgrade the GPU later in the year as this will be a very good foundation for a system.
PCPartPicker part list:
https://uk.pcpartpicker.com/list/z9Fv3b
Price breakdown by merchant: https://uk.pcpartpicker.com/list/z9Fv3b/by_merchant/
CPU: Intel - Core i5-8400 2.8GHz 6-Core Processor (£143.99 @ Aria PC)
Motherboard: ASRock - B360M Pro4 Micro ATX LGA1151 Motherboard (£64.99 @ Overclockers.co.uk)
Memory: Team - Vulcan 16GB (2 x 8GB) DDR4-2400 Memory (£134.99 @ Overclockers.co.uk)
Storage: Samsung - 850 EVO-Series 500GB 2.5" Solid State Drive (£102.95 @ Aria PC)
Case: Phanteks - Eclipse P300 Tempered Glass ATX Mid Tower Case (£47.94 @ Aria PC)
Power Supply: Corsair - TXM Gold 550W 80+ Gold Certified Semi-Modular ATX Power Supply (£63.21 @ CCL Computers)
Total: £558.07
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-05-18 15:14 BST+0100
Facebook
Twitter
Instagram