On the second hand market I would hope to pay £400 for a laptop with a 10th gen i5, a RTX 2060 and a 1080p 144Hz screen. Looking at Ebay, that is realistic yet hard to find as a lot of sellers seem to be excessively optimistic.. You might have better luck with Facebook marketplace or Craigslist.
"refurbished" laptops are generally just second hand laptops that have been given a wipe, tested and put up for sale with a short warranty. The main benefit over buying directly from the previous owner really is the warranty, but you really are paying a premium for it. That might affect your ability to afford a reasonably spec'd laptop within your budget.