Best monitor for around £500

I have a budget of around £500 for a new monitor my main this is doing uni work but I do want to game on it aswel like console and pc games. I play things like assassin's creed and uncharted. I use mainly the PS4/5 and occasionally the PS3 but also my Pc and intend to watch movies and football on it aswel plus uni work. Please give me the best monitor possible for this purpose and price but ideally not oled as the whole bleed out thing kinda makes me concerned.

What's your PC spec? That will dictate whether it makes sense to chase higher refresh rates or not.
Any preference on size?
Do you have an audio system that you want to use already?

I don't really have an audio system but I'm not too bothered I can just connect my headphones or Alexa. I dunno my pc spec lol because it's my cousin's I just borrow it but even if the monitor is a high refresh rate does it matter can't it still handle lower refresh rates? Ideally 27-32 inches

It's not that having higher refresh rates would be an issue, it's that when it comes to prioritising features for your budget it could mean spending money for one thing at the expense of another. For example if there were two choices vying for the top spot, one a 4K monitor with high refresh rates and the other a 4K monitor with exceptional HDR, it wouldn't make sense to pick the high refresh rate monitor if that wasn't going to provide any practical benefit.
With that said, in looking for options I think I've found something that ticks every box as well as you could hope for at under £500- 4K and 160Hz so you can choose between the performance and fidelity modes of PS5 games and just let whatever PC you use go as high in res/refresh as it can, and while it's only an IPS panel like most monitors of this price point, it's a very good panel for image quality and is also ini LED backlit, which is very rare to find in 4K/120Hz monitors at this price point and grants excellent contrast and HDR. It's the next best thing to the OLED and QLED monitors that sit outside your budget range. Reviews for it all look extremely positive even when reviewed at it's higher RRP. If you want to spend this much on a display that will cover all bases, I would jump on this while it remains in stock.
https://www.overclockers.co.uk/cooler-master-tempest-gp27u-27-3840x2160-ips-160hz-freesync-hdr-hdmi-2.1-wi-mo-006-cm.html

I don't really know that brand I can stretch my budget slightly if it means a much better monitor. I'm mainly thinking Acer Asus or Samsung anything from them you'd recommend?

If the monitor is better I don't mind the stretch of budget but I'd say £650 is my max unless there's an incredibly good monitor for £700 any suggestions ideally from the brands I listed

https://www.samsung.com/uk/monitors/gaming/odyssey-neo-g7-g75nb-32-inch-165hz-1ms-curved-uhd-4k-ls32bg750npxxu/
Samsung have this monitor which has pretty much the same specs and features as the Coolermaster one above, only in a 32" size and £170 more expensive.
Beyond that, I can't see anything from your preferred brands with a better spec sheet or even matching the Coolermaster for under £700, you're probably going to need another £100 on top of that or to concede on features in some way- the Coolermaster really is that good.

Is this any good https://www.currys.co.uk/products/lg-ultragear-32gr93ub.aek-4k-ultra-hd-32-ips-gaming-monitor-10251826.html?istCompanyId=bec25c7e-cbcd-460d-81d5-a25372d2e3d7&istFeedId=4d7eb93e-055f-499d-8ee5-1cdcc50d67d1&istItemId=lwxmittql&istBid=t&srcid=198&cmpid=ppc~gg~0075+(Shopping+Ads)+Gaming+Monitors+-+PMAX~~Exact~71700000115259416~&mctag=gg_goog_7904&kwid=GOOGLE&device=m&ds_kids=&tgtid=0075+(Shopping+Ads)+Gaming+Monitors+-+PMAX&&gad_source=1&gclid=CjwKCAjwktO_BhBrEiwAV70jXuwTTk4eEoCJEoRWDReX_wWpD6GR-KL_k7pKkmS7Oo7seny_pYcblhoCIIIQAvD_BwE&gclsrc=aw.ds

It's perfectly decent, but again, worse than the Coolermaster- it's a conventional IPS panel without the mini LED backlighting that provides a substantial boost to peak brightness, HDR quality and contrast. You'd be paying £100 more for worse image quality, just for the brand.
If you're a student, you may be able to get 20% off the Samsung I linked to previously which would make it a better display than this LG for a little bit cheaper. Check the webpage, it's under the price/finance info.

Ok I'm thinking cooler master then but the website you sent I've never heard of any known brands like Argos Currys?

Nope, nobody else is selling it for anywhere close to this cheap. However Overclockers are a well established and reputable brand that have been in business for over 20 years in the UK, and I have been personally buying from them and recommending them on sites like TSR (I used to be one of the moderation staff here on a previous account) for over a decade. Like lots of specialist tech and PC building companies, they don't have a high street presence to keep their costs down, but they are very well known and well regarding for a retailer or this type.

I found this on sale and seen some good reviews about it.
https://www.currys.co.uk/products/lg-ultragear-27gr93ub.aek-4k-ultra-hd-27-ips-lcd-gaming-monitor-black-10269671.html what do you think