BF3 will really struggle on that.
For a £350 budget I dont really know what else to suggest though. I couldnt do much better for £350 but at the same time I wouldnt even try to build a gaming system for that.
Only advice i could say would be go for an AMD, maybe phenom or llano build, save money on the cpu and then upgrade the graphics to a 7770 or a 6850/6870, but that may break the budget limit.
Also, the psu probably wouldnt be enough, and I wouldnt ever use an unbranded one. Other than look for second hand parts on ebay, I dont know what to suggest
Not sure whether this is right or not... I have a mate who uses a 6770 for BF3 and he plays on medium or even high sometimes with decent frame rates. 6770 is more than ample in my opinion.