Well, Amazon have a 120mm ID-Cooling one for £26 with a black top plate:
Buy ID-COOLING SE-224-XT Basic CPU Cooler AM4 CPU Cooler 4 Heatpipes CPU Air Cooler 120mm PWM Fan Air Cooling for Intel/AMD at Amazon UK. Free delivery and return on eligible orders.
www.amazon.co.uk
Arctic Freezer 34 is easy to find in the UK and about £30 after tax. CM 212 black edition also similar price and a very clean aesthetic.
Nothing wrong with the Pure Rock 2 Black either but at that price you're paying for looks not performance, and getting into the territory of better coolers and better support. Only 50% more money gets you the Noctua NH-U12S Chromax Black and that's a higher-quality, higher performance product that will get you infinite free socket upgrades. I've been using my NH-U12 for 15 years now on my fourth (free) socket kit and it's still a better cooler than anything under £40. At £40-50 you should be able to find options with larger heatinks, or more heatpipes, and proper machined baseplates rather than cheap direct-contact cooling...
It's really hard to guage as dBa measurements aren't standardised so one manufacturer's 38dBA is not necessarily as loud as another manufacturer's 38dBA. The quality of the noise matters almost as much since some fans produce noise across a wide spectrum of frequencies that makes them hiss unobtrusively whilst others have an peak at a particular frequency that stands out clearly from other background noise. Additionally, your hearing is very good at ignoring sounds below the ambient noise floor so the amount of background noise in your room has a big impact on how noisy your perception of something is.
TL;DR is that you really can't use dBA measurements from manufacturers. Better to find a single review site with standardised testing of the models you're interested in and use their tests (which will be fair and use identical measuring methods across all coolers) to give you a better idea of which ones are quietest.