An overclocked 8320 and an overclocked 3570k perform on par depending on the game. Some games will show better performance on the 8320. I think it is safe to say that more titles are coming out to accommodate more cores but in terms of performance in gaming, i rate them about the same, perhaps a few fps' more on the i5 but that doesnt matter on your budget if you look at it like this:
You can spend 209 pounds now and get the 8320 and motherboard and not have to touch them for a few years. Maybe steamroller platform will come out on AM3+ but no one knows at the moment so i wouldn't count your chickens. 6 months down the line buy a 7950 or the (equivalent new card that is out next month) and BOOM you got a nice gaming rig there that will max stuff on 1080p
OR
You can spend 216 pounds on a rig which will cripple high CPU games until you can dish out another 185 quid for the i5 (which will prob cost more in 6 months). So 6 months down the line, you have spent just over 400 pounds on a cpu and motherboard when you could have got almost the same performance in CPU and a decent graphics card to go with it.
Go with the AM3+ platform for this budget, what you save here will give you far more FPS when you spend it on a graphics card. If you really want the i5, forget getting a brand new i3 now and wait a while before you upgrade again.
Not fanboying here, if you can stick to your current set up until you can buy the i5 straight off, do it. Just think its counter productive spending for an i3 which will be scrapped 6 months down the line, when you need a graphics card aswell.