Does the Hyper 212 Evo fit in the NZXT Phantom 410?

Solution
Yes. It can take coolers up to 170mm, the EVO is 158.5mm so you'll have 11.5mm to spare, give or take a couple of mm.

byza

Honorable
I made a few adjustments to your build. You were skimping on the mobo so i put in a better one, faster RAM and a lower wattage PSU. The 850w was more than you need for a single card, but not enough for crossfire, so there is no reason to get it. In the end it's about 12 pound more, but it's a more balanced build.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4690K 3.5GHz Quad-Core Processor (£166.98 @ Scan.co.uk)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler (£24.25 @ Scan.co.uk)
Motherboard: ASRock Z97 EXTREME4 ATX LGA1150 Motherboard (£105.56 @ Scan.co.uk)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-2133 Memory (£63.60 @ Kustom PCs)
Storage: Samsung 840 EVO 120GB 2.5" Solid State Drive (£57.19 @ Aria PC)
Storage: Western Digital BLACK SERIES 1TB 3.5" 7200RPM Internal Hard Drive (£55.55 @ Amazon UK)
Video Card: Sapphire Radeon R9 290 4GB Tri-X Video Card (£295.55 @ Scan.co.uk)
Case: NZXT Phantom 410 (Black/Orange) ATX Mid Tower Case (£75.41 @ CCL Computers)
Power Supply: EVGA 750W 80+ Gold Certified Fully-Modular ATX Power Supply (£80.90 @ Amazon UK)
Optical Drive: LG GH24NSB0 DVD/CD Writer (£14.89 @ Amazon UK)
Total: £939.88
Prices include shipping, taxes, and discounts when available