It’s mahoosive for you. If you want second hand look for a 54cm Cannondale/Trek, a Medium Giant, or even Small if thinking of a Cyclocross bike.
Virtual Top Tube is the standard measure, so look for bikes with a VTT of about 53-54cm. Tables are widely available on the web. A cm lower or higher can be accommodated by a change in stem, but for you I’d be starting with a 100mm stem on a 53cm, but might expect a 90mm will be a better fit. Shops will ofetn swap for free – even on used bikes.
£500 buys a very good SH bike, Look for Alloy at that price with 105 or Ultegra groupset.