alphawhisky

Those are much better temps. Nice one.

Thought I'd post a quick update as I finally had a chance to look at the set-up. I wanted to post an update, particularly for other newbies in the same situation – perhaps my "lessons learned" will be of help to others(!)
If you're a newbie, try building a PC. It's stressful but fun! Lots of great advice online, so just read-up and take your time. When folks like @tkitch suggest you might have screwed up your cooler install, listen to them. (Turns out, I did). I'd not only mounted the fan the wrong way in the cooler, but also realised that after initially applying the thermal paste, I took the cooler off and then re-attached it. Seems this is a giant no-no.  I cleaned the thermal paste off, re-applied the cooler (with correctly oriented fan), re-enabled PBO and CPB, and then checked what my temps were like. Running a 10 min run in Cinebench saw temps hit a max of 58c (compared to 95c before!) Thereafter, temps quickly return to a cool-ish 32c. Very happy with that (and, if I can figure out how, I guess there may be scope for some mild overclocking!) 
 
Thanks to everyone who replied and kept me on the right track. 

Try taking the side/glass panel off to see what the temperatures difference. I'm not sure how your setup is, but from the pictures I have seen of the case it just could be the front upper half of the case it restricting the air intake. It looks like upper front fans can pull air in from the sides if the fan are mounted further inside of the case.

Yep! AMD's own spec is 95C max under boost. And AMD's Director of Technical Marketing said: "Yes. I want to be clear with everyone that AMD views temps up to 90C (5800X/5900X/5950X) and 95C (5600X) as typical and by design for full load conditions. Having a higher maximum temperature supported by the silicon and firmware allows the CPU to pursue higher and longer boost performance before the algorithm pulls back for thermal reasons,"
 
Article by PCGamer here: https://www.pcgamer.com/amd-views-ryzen-5000-cpu-temperatures-up-to-95c-as-typical-and-by-design/

but why? it’s not worth it for any use case over the 5600 except XOC. @PDifolcoand @alphawhiskyare correct. If the build needs more CPU performance than a 5600 a 5700x is a smarter upgrade.

I would go with a 5600X instead. You can definitely get a better PSU as well, that'll help carry over for when you get your next gpu too. Building the pc is going to be cheaper than a pre-built, and with pre-builts they tend to cheap out on certain components like the memory, case, motherboard, etc.
 
https://uk.pcpartpicker.com/list/g7v6d9

Thoughts on performance of the 5600 vs my existing i7-6700? Worthy upgrade path? Would be defo better like +50% faster all over the board, less stutters, etc, and cheap Could save a buck by keeping my existing PSU (Thermaltake Smart RGB 80+ White 700W) though I'd prefer a fully modular PSU if possible...  Yes, you don't need to upgrade the PSU. BTW you could get a cheaper NVme like a SN570 (a few bucks less) Is the included cooler with the Ryzen good enough? Yes it's fine but you can add a £30 ish cooler to get better temp/less noise I've done PC upgrades previously, but never built my own system. Is it worth waiting for Black Friday for a budget pre-built?  dunno... And, on a similar theme, do you think component prices will drop significantly during Black Friday itself?  dunno...

Well, the 3600 non X comes with the smaller stealth so it may be just dumb people trying to overcloxk on the smallest cooler. 3600X should be fine. If you're worried, a cheap solution is the Arctic Freezer eSports 34. It's about 30$ and will keep the CPU very chilly.
 
As for the board, you do get a better VRM for future upgrades to 12/16 cores and a better BIOS. Imo it's a worthwhile investment but make sure to look at the motherboard tier list on the forum here. You could end up finding a cheaper ASRock X570 board that also fits the budget and offers superb quality.
 
Now, the PSU. I'd strongly suggest upgrading to a Corsair CX550 or Be Quiet System Power 9 at the minimum. The Thermaltake Smart series is notoriously bad and unstable under load. You likely don't want to end up with a dead board or GPU again cause the PSU shit itself for no reason. Sell the Smart and get a good reliable power supply