Generally for ultra-settings AAA gaming, a GTX 1070 would be an "entry-level GPU" for 1440p, that is, you may have to decrease some in-game graphics settings in order to achieve constant 60fps esp. on GPU-intensive games. A GTX 1080 would definitely be a worthwhile upgrade if you want to max. out most, if not all, games in that resolution. The GTX 1080 Ti, on the other hand, would be best if your 1440p monitor can do 120~144Hz, but you have to shell out a lot of money for this card. Price/performance, I would personally get a GTX 1080 if I was in your situation.
Having said that, your current rig will definitely be faced with bottlenecking issues (i.e., the weak CPU hindering the maximum possible performance of the powerful GPU, esp. if the game is CPU-intensive.) Though a quick fix might be to decrease in-game graphics, spending for an expensive beefy GPU will be for naught if you can't maximize its full potential.
The FX series, in all honesty, is a dead-end upgrade path, now that the Ryzen series have been released. Your current FX 8350 CPU would choke a
GTX 1080, a
GTX 1070, and to a certain extent, even a
GTX 1060.
(Source: http://www.tomshardware.com/forum/id-3192807/ultimate-bottlenecking-guide.html)
As you mentioned that we can assume you have a budget of £1000-1200, then my recommendation is to upgrade your CPU, MB, and RAM alongside the GPU you want for best (balanced/non-bottlenecking) pairing.
If you intend to overclock, here is a suggested CPU + CPU Cooler + MB + RAM + GPU (Note that the suggested build below is limited to parts mentioned, the remaining budget can be used for other parts not mentioned such as the PSU, Case, SSD/HDD, or other components you don't have yet -- I did not include these latter parts as I assume you already have them on your current PC):
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-7600K 3.8GHz Quad-Core Processor (£221.59 @ Aria PC)
CPU Cooler: be quiet! Dark Rock Pro 3 67.8 CFM Fluid Dynamic Bearing CPU Cooler (£67.48 @ Amazon UK)
Motherboard: Asus STRIX Z270F ATX LGA1151 Motherboard (£161.48 @ CCL Computers)
Memory: Corsair Vengeance LPX 16GB (2 x 8GB) DDR4-3200 Memory (£125.47 @ Scan.co.uk)
Video Card: EVGA GeForce GTX 1080 8GB Superclocked Gaming ACX 3.0 Video Card (£505.47 @ Scan.co.uk)
Total: £1081.49
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-04-07 19:14 BST+0100
If you don't intend to overclock, here is a suggested, less expensive, alternative:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-7500 3.4GHz Quad-Core Processor (£173.94 @ Aria PC)
Motherboard: MSI B250 PC MATE ATX LGA1151 Motherboard (£80.98 @ Ebuyer)
Memory: G.Skill Ripjaws V Series 16GB (2 x 8GB) DDR4-2400 Memory (£102.60 @ Aria PC)
Video Card: MSI GeForce GTX 1080 8GB GAMING X 8G Video Card (£525.90 @ Alza)
Total: £883.42
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-04-07 19:23 BST+0100
Assuming the budget you have is for an entire (overhaul) new PC, then here is another suggested parts list (excluding OS and peripherals):
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-7600K 3.8GHz Quad-Core Processor (£221.59 @ Aria PC)
CPU Cooler: CRYORIG H5 Universal 65.0 CFM CPU Cooler (£55.89 @ CCL Computers)
Motherboard: Asus PRIME Z270-P ATX LGA1151 Motherboard (£109.62 @ CCL Computers)
Memory: Corsair Vengeance LPX 16GB (2 x 8GB) DDR4-2400 Memory (£104.99 @ Amazon UK)
Storage: Western Digital BLACK SERIES 1TB 3.5" 7200RPM Internal Hard Drive (£72.94 @ Eclipse Computers)
Video Card: MSI GeForce GTX 1080 8GB Video Card (£479.99 @ Amazon UK)
Case: Cooler Master MasterBox 5 (White) ATX Mid Tower Case (£49.98 @ Amazon UK)
Power Supply: Corsair RMx 650W 80+ Gold Certified Fully-Modular ATX Power Supply (£91.97 @ Amazon UK)
Total: £1186.97
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-04-07 19:34 BST+0100
Hope these suggestions help