Still pretty vague on the budget, but I suppose why not, I have extra time this morning anyway.
Okay, so PSU is Cooler Master MWE500. Will do the job, but it is a budget unit so it could do with being replaced. Case, also kinda fine but also kinda on the budget side. I'd for sure just buy a new case and PSU if you were to build a new system, though if you just upgrade they can both potentially be re-used. I wouldn't re-use the PSU with anything higher end than a GTX 1660Ti though, and the case is really up to you- just had to know what motherboard form factors you'd be able to fit in it since I wasn't sure if you had an mATX or ATX case- it's ATX btw.
If you upgrade, then you have a bunch of options to be honest.
For CPU, you could pick up a used i5 or i7 that will fit your motherboard, something like an i5-6500/7500 or i7-6700/7700 would do nicely. However, at this point, I'd honestly be really considering Ryzen. Even with a new motherboard, you could upgrade to Ryzen for about the same price as upgrading to another Intel CPU with your current motherboard. Benefits with Ryzen are the extra cores/threads and upgradability is better. Sticking with your current mobo is probably the easier option though. A used i5-6500/7500 shouldn't be any more than 70 quid. People are still asking £150ish, sometimes even more for their used i7-6700/7700's though. I've seen them go for £120ish before. You can easily find used R5 1600's for like £80, and B350 mobo's for less than £50 no problem. The Intel option just is a really hard sell at this point IMO, even with already having the LGA1151 mobo. If it was a Z270 mobo, then maybe a 6700k/7700k would be a good shout.
For GPU, I'd be holding on to that 1050Ti for now to be honest, you should really be upgrading that monitor at the same time as GPU IMO. If you do want a simple GPU upgrade with your current monitor, then a GTX 1660 would be more than adequate tbh. If you upgrade monitor, I'd be aiming for 1440p 144Hz, or maybe ultrawide. At that point, I'd be looking at an RTX 2060 at least. Thinking of picking up an RTX 2060 myself since I'm impatient, not sure I can keep holding off for Navi.
Definitely add an SSD. 480-512GB SSD's are easy to pick up for 50 quid these days, incredible value so I wouldn't even bother with anything smaller unless you have a really tight budget. Honestly, even SSD's in the 1TB range are really good value these days. You also might want to add another 8GB RAM, especially since it's a heck of a lot cheaper than this time last year.
Like I said though, if budget is truly no concern, then since this is a fairly low-end system, you'd probably be better off with a whole new build. We'd definitely need less vague info on budget for this though, since there are just so many possibilities. If it were me, and I were building a new PC right now from scratch, for gaming, then it'd probably be something like this;
PCPartPicker part list / Price breakdown by merchant
CPU: AMD - Ryzen 5 2600 3.4 GHz 6-Core Processor (£144.98 @ Amazon UK)
CPU Cooler: be quiet! - Dark Rock 4 CPU Cooler (£52.98 @ Novatech)
Motherboard: MSI - B450 TOMAHAWK ATX AM4 Motherboard (£89.98 @ Amazon UK)
Memory: Corsair - Vengeance LPX 16 GB (2 x 8 GB) DDR4-3000 Memory (£81.18 @ Aria PC)
Storage: Intel - 660p Series 1 TB M.2-2280 Solid State Drive (£108.99 @ Ebuyer)
Video Card: MSI - GeForce RTX 2060 6 GB GAMING Z Video Card (£369.99 @ Amazon UK)
Case: Phanteks - ECLIPSE P600S ATX Mid Tower Case (£130.00 @ AWD-IT)
Power Supply: Corsair - RMx (2018) 550 W 80+ Gold Certified Fully-Modular ATX Power Supply (£73.32 @ Ebuyer)
Monitor: Samsung - LC27JG50QQNZA 27.0" 2560x1440 144 Hz Monitor (£289.96 @ CCL Computers)
RTX 2060 will do well at 1440p 144Hz with optimised settings, but if you're adamant on spending more, then RTX 2080 would be an alright shout I suppose. P600s is a bit on the expensive side for a case to be fair, plenty of nice options in the £70ish range, like the Fractal Meshify C, NZXT H500, or Eclipse P350x. I'd personally also probably spend more on a motherboard, but I tend to go overkill on mobo and hate using anything other than Asus' BIOS in my personaly systems lol, so I usually pay the Asus premium- that said I have an MSI AM4 mobo currently. The B450 Tomahawk is perfectly fine for the R5 2600, and MSI's BIOS is definitely far from the worst but I don't love it.
This list is far off the 5-10k you're apparently willing to spend though, of course, so if you really want to go that route, we just need more information to help properly. Beyond £1500-2000, you're looking at an enthusiast grade system(even if doesn't necessarily have enthusiast grade components) so we need to know what ticks your boxes, if you get me. What you want to make it your own, like maybe there's a specific case you'd like or maybe you want RGB LEDs all over the place that are all synced up together- or maybe no LEDs whatsoever. Maybe you want a custom loop, or a nice RGB AIO, or maybe you'd just prefer to stick with a nice air cooler? Maybe you want to drop more than a rack on a 2080Ti. 2080Ti is literally just for the e-peen though tbh, not that I wouldn't if I could afford one lmao. You also have to ask yourself if you want to pay the Intel premium for something like a modern i7, or even i9-9900k. Or maybe you want to go HEDT CPU for the bant.