To be fair we will need new RAM as well I'm not sure yours is really running at 3000 MT/s ? DDR3 didnt go there AFAIK outside of maybe some extreme overclocking sets. Generally Haswell capped out around 2400 IIRC.
Assuming as
@Oussebon said your PSU is of a serviceable quality which is definitely something you should look into, I'd suggest something like this.
PCPartPicker Part List
CPU: AMD Ryzen 5 1600 (14nm) 3.2 GHz 6-Core Processor (£103.98 @ Amazon UK)
Motherboard: MSI B450 TOMAHAWK MAX ATX AM4 Motherboard (£109.98 @ Amazon UK)
Memory: G.Skill Ripjaws V 16 GB (2 x 8 GB) DDR4-3600 Memory (£112.10 @ Newegg UK)
Video Card: PowerColor Radeon RX 5700 XT 8 GB Red Dragon Video Card (£379.97 @ CCL Computers)
Total: £706.03
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2020-05-12 14:40 BST+0100
You don't need X570, its advantages are PCI-e 4 which is only useful if you are often transferring large files from and to your NVME SSD. And compatibility with AMD's next gen processors, which while nice is not inside the budget.
The
Ryzen 1600 AF I picked is basically the same as the Ryzen 2600. Its a very good chip especially for the price offering 6 cores and 12 threads. While benchmarks show Intel are 10% ahead of AMD in games, remember that this is for the most part when reviewers test a 2080 TI at 1080p. Its not realistic, and in a blind test at 1440 high settings and above there's no perceptible difference. Going forwards the extra threads are going to be a better choice as well IMO.
I picked a 5700XT, its the cheapest model with a decent cooler here. T
he Asus TUF is not a good card that doesnt cool well, that's why you find it cheap everywhere. On the Nvidia side, the 2060 is comparable in price but the 5700XT performs around the same as a 2070, non super. IMO RTX performance is not yet mature enough to justify the extra cost.
If you're set on an Intel/Nvidia build, this would also be an option, or you could switch out the 5700XT for a 2060/2060 Super if you'd prefer. Although I believe the above is better overall.
https://www.youtube.com/watch?v=OJU8jKIYtS4
PCPartPicker Part List
CPU: Intel Core i5-9400F 2.9 GHz 6-Core Processor (£139.98 @ Aria PC)
Motherboard: Asus PRIME Z390-P ATX LGA1151 Motherboard (£111.18 @ CCL Computers)
Memory: Corsair Vengeance LPX 16 GB (2 x 8 GB) DDR4-3200 Memory (£74.97 @ Laptops Direct)
Video Card: Gigabyte GeForce RTX 2060 SUPER 8 GB WINDFORCE OC Video Card (£389.99 @ CCL Computers)
Total: £716.12
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2020-05-12 14:58 BST+0100
If you wanted to bring the cost more towards the middle of the budget I'd suggest dropping the graphics card down to a lower tier, but of course you'd then want to temper your expectations of what kind of settings to use in game if you wanted to keep the FPS closer to 144hz.
Finally I believe that all the components should fit, but you should definitely double check the exact model of your case against the length of the graphics cards you choose, and most certainly at very least be sure that your PSU is capable of providing most of its 550Watt capacity on the 12v rails. If your PSU blows up it may well take everything else with it.