I can't find a laptop or mini PC which meets the GPU requirements for Palia at £300. Looks like you really need a dedicated graphics card to be guaranteed to run it.
What I will say is that this has the same spec as my Daughter uses to play Genshin Impact which has similar system requirements.
This also doesn't meet the minimum specs but still runs the game, albeit the frame rate does drop at times: https://www.laptopstation.co.uk/products/hp-laptop-14s-dq2512na-11th-generation-core-i5-8gb-ram-256gb-ssd-14-fhd-screen?_pos=2&_fid=a1e5c204d&_ss=c
So, this may run Palia, but no guarantees. If you do want to guarantee then it will require a larger budget, such as for this: https://www.laptopstation.co.uk/products/asus-tuf-fx506lh-h-series-core-i5-8gb-ram-512gb-ssd-nvidia-gtx-1650-15-6-fhd-screen-gaming-laptop