Something you need to understand about turntables is they are not a technology that is still making progress. The peak of turntable technology came in roughly the 1982-1986 timeframe... and those '80s technologies (computer-controlled linear tracking tonearms and such) aren't even used anymore because they are super complicated to make, and the economies of scale needed to make them worth producing just no longer exist. Most modern turntables are built around technology from the mid to late 1970s. So the original version LP60, which came out in 2009, is in no way outdated compared to now. A 2009 turntable and a 2023 turntable are made with all the exact same bits.
That said, while it's not outdated, it is still exactly what it was in 2009: a hollow plastic starter turntable with a cheapo spring force tonearm, no adjustability, and essentially no upgrade path. If you can spend £300 for your system, that is enough to get you something that is a notch nicer, with adjustable tracking force, a removable cartridge, and a proper counterweighted tonearm... something that would work better out of the box, and would also be able to take a few upgrades so you won't outgrow it as quickly.
If £300 is an absolute hard cap, get these.
https://www.amazon.co.uk/ANGELS-HORN-Bluetooth-Turntable-Cartridge-Orange/dp/B09P8GPDHP £155
https://www.amazon.co.uk/Edifier-Powered-Monitor-Speakers-Near-Field/dp/B0BV39DPNB £120-130 depending on color
And if you can spring for more like £350, it might be advisable to get passive speakers and a basic amplifier instead. For example, this amp for £60 plus one of these these sets of speakers:
https://www.amazon.co.uk/POLK-AUDIO-High-Resolution-Loudspeakers-Performance/dp/B09BMXVQFT
https://www.audioaffair.co.uk/wharfedale-diamond-10-1-speakers-pair