I'd probably look into getting a new monitor the first half of next year. In regard to budget, I'm not sure. I wouldn't be looking to spend ridiculous amounts, but it'd definetely have to be something that compliments the power the rig.
For something to complement the RTX 2080 you'd be looking at £500~ or more (i.e. 1440p gsync, 4k gsync). There were already rumours that the RTX 2000 series was a quick whip-round of consumers by Nvidia with a new lineup coming next year. There are also rumours of AMD releasing GPUs competing with RTX 2070/2080 for half the price.
I'm very concerned you'll find yourself spending £800 on a GPU that might be on the verge of obsolescence by the time you come around to actually using its potential.
Also, Intel CPU prices have gone up a lot due to supply issues, such that an i7 build is maybe £100-200 more than an AMD R7 build, while offering maybe a few % more performance at 1440p, even less at 4k. The kind of difference you're not going to notice with the naked eye.
I'd suggest a system with a GTX 1070 ti, which is very similar to the GTX 1080/ RTX 2070 but almost £400 less expensive (almost £120 less than the RTX 2070 too).
Even with a better motherboard, a better PSU, and a better SSD, this makes the build £500 less, letting you afford a 1440p 144hz monitor with gsync (the Dell S2716DG has been popular on these forums and is usually available for ~£450).
Case
FRACTAL FOCUS G BLACK GAMING CASE (Window) Processor (CPU)
AMD Ryzen 7 2700X Eight Core CPU (3.7GHz-4.35GHz/20MB CACHE/AM4) Motherboard
Gigabyte X470 AORUS Ultra Gaming: ATX, USB 3.1, SATA 6GBs - RGB Ready Memory (RAM)
16GB Corsair VENGEANCE DDR4 2933MHz ~ (2 x 8GB) Graphics Card
8GB NVIDIA GEFORCE GTX 1070 Ti - DVI, HDMI, 3 x DP - GeForce GTX VR Ready!
---FREE Geforce Fortnite bundle w/ select GTX cards 1st Storage Drive
2TB SEAGATE BARRACUDA SATA-III 3.5" HDD, 6GB/s, 7200RPM, 64MB CACHE 1st M.2 SSD Drive
500GB WD Black™ M.2 NVMe PCIe SSD (up to 3400MB/s R | 2500MB/s W) DVD/BLU-RAY Drive
NOT REQUIRED Power Supply
CORSAIR 650W TXm SERIES™ SEMI-MODULAR 80 PLUS® GOLD, ULTRA QUIET Power Cable
1 x 1 Metre UK Power Cable (Kettle Lead) Processor Cooling
CoolerMaster Hyper 212X (120mm) Fan CPU Cooler Thermal Paste
STANDARD THERMAL PASTE FOR SUFFICIENT COOLING Sound Card
ONBOARD 6 CHANNEL (5.1) HIGH DEF AUDIO (AS STANDARD) Wireless/Wired Networking
10/100/1000 GIGABIT LAN PORT (Wi-Fi NOT INCLUDED) USB/Thunderbolt Options
MIN. 2 x USB 3.0 & 2 x USB 2.0 PORTS @ BACK PANEL + MIN. 2 FRONT PORTS Operating System
Genuine Windows 10 Home 64 Bit - inc. Single Licence [KUK-00001] Operating System Language
United Kingdom - English Language Windows Recovery Media
Windows 10 Multi-Language Recovery Image - Unlimited Downloads from Online Account Office Software
FREE 30 Day Trial of Microsoft® Office® 365 (Operating System Required) Anti-Virus
BullGuard™ Internet Security - Free 90 Day License inc. Gamer Mode Browser
Microsoft® Edge (Windows 10 Only) Warranty
3 Year Silver Warranty (1 Year Collect & Return, 1 Year Parts, 3 Year Labour) Delivery
STANDARD INSURED DELIVERY TO UK MAINLAND (MON-FRI) Build Time
Standard Build - Approximately 6 to 8 working days Quantity
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