The new motherboard + new cpu combined cost is not a worthwhile upgrade. I would keep the CPU and spend the rest on a good GPU, you could get a 7870 with the savings and that would make your rig boarderline high end.
The only worthwhile cpu upgrade is gonna be an 83xx or an i5/i7. If you're not doing that, go all out 7870. Heck, if you were planning on getting a 150$cpu+100$motherboard+100$ graphics card anyway. I'd say 300$ for a 7950 is a worthwhile investment, then again you're not a 'serious' gamer so i don't kn ow if that would be best. A 7870 can be had for 180$, and you could still theoretically upgrade your cpu if you can find a 1080T, it's an AM3 socket 6 core phenom so you wouldnt need a motherboard.. Neck in neck with an i5 2500k. And better in games/apps that use all cores.
To be 100% honest with you, AMDs processors aren't as good as they used to be - I've looked around and its hard to find even a motherboard with AM3+ that supports PCI-e 3.0. If you have enough money, what I'd do is invest your cash in a Intel Core i5 (possibly unlocked?) and a 7870, because honestly, the 7770 is very poor in overall gaming performance.
Okay, that's interesting. Considering that my budget is absolute tops £350, I could either spend £300 on a 500GB HDD, 8GB RAM, HD7850 OC 2GB and a 970 Mobo, or Just spend £330 and get an i5 3570K and Z77 Motherboard, but I'd have to keep the 5670. What's my best option? i5 3570K + HD5670 512MB OR Phenom II X4 + MSI Twin FrozR III 2GB?
I say i5 3570K with a Z77 mobo, BECAUSE that processor will last you YEARS before having to replace it - it's like owning a Core 2 Quad that you can overclock - you don't have to replace it because its such a solid processor and has such good connectivity with modern hardware. Save up and maybe you'll be able to get in on AMD's next generation GPUs!