I have done under 1" with irons, though it is hard and a lot of factors need to be in your favour (I would struggle to do that today, haven't practiced much recently). Personally I shoot better with irons than a scope for whatever reason (but I basically only shoot irons and I despise shooting scopes so that could just be why).

I remember a few years ago they had this little rifle competition in town when a new gun store opened up with a deck of cards as the target (about 100 people ended up shooting, and you could go for multiple rounds if you paid the fee again). Top three hands got prizes. For most of the day with my iron sighted K31icon I was in 3rd place, even though most (maybe all) my competition was using scoped rifles. Apparently I was beat out in the last couple hours (I had long left by that point), but it shows its more about the user than it is the equipment.

In terms of how what is good accuracy, I guess it depends on a lot of factors. Type and quality of ammo, the type of rifle (i.e. is it a Lee Enfield, Mosin Nagant, K31, Mauser, etc.), condition of the rifle, etc. Generally I find most military surplus rifles in average condition tend to be able to do 2-4" groups, which was roughly the standard of the era.