Indeed you could get one second hand, such as an older Thinkpad T series or an HP business class machine, or a Dell Latitude. Actualy you could probably get a new Dell Vostro (which aren't bad, but not as nice as Latitudes) for your budget at the Dell Outlet or at least close to it. By the time VAT is added on you will probably need circa 400 pounds for that.
You can easily buy a new laptop for 300 pounds, but when you say high quality I am taking that literally, you wont get quality machines for that, just plastic fantastic stuff ...which tbh would probably be fine.