If you are thinking of dipping your toe into SS riding I would seriously consider buying second hand rather than used.
For any given budget you will be able to pick up a better quality bike and, if you don't get on with this type of riding, you should be able to sell it on again without ending up out of pocket too much. Of course, a bit more mechanical knowledge and the ability (or help from more experienced riders) to spot good/bad bikes might be useful.
On that note, I would also suggest the Genesis range. Their "Flyer" models are around £600 new, but I have seen them listed at less than half that on
eBay and in local, private adverts. They also fit your request for wider tyres - they come with 28mm rubber fitted and could go a fraction wider (32mm possibly) if you ditch mudguards. At this width there are a variety of nobbly options available. Of course, if you need a model that is a bit more robust in the frame, their Day One models might fit, and I have even seen a few of their Croix models converted for SS on the second hand market.
Hope this helps,
J