I'll echo much of what has been said about fixed S&B scopes etc above.
However, my .243 had a £250 second hand Leupold 3-9X50 on it, and it was perfect for what I used it for (roe and foxes). So much so that I now have that scope on one of my .270s.
I think the sensible approach is to decide on a price ceiling (sounds like £350 is yours), then draw up a short list of the brands you'd be happy using. My own personal, idiosyncratic list, based on what I've used and like, is S&B, Leupold and Meopta. I dislike Zeiss and think Swaro is overpriced. Then keep an eye out for ANY scope made by them in the range 6x42, 8x56, 3-9x50, 4-12x50, 7x50 (all will work perfectly well for what you need). Then take the first scope in good condition that meets all those criteria and stop worrying.
You do not need IR or side focus etc etc. Tube size does not matter. Make sure you get standard reticules (a4, a7, duplex), and not something odd, like German No1 post.