Ok after looking through, I think this is a good motherboard:
Gigabyte GA-MA785GMT-UD2H 785G Socket AM3 DVI VGA HDMI Out 8 Channel Audio MATX eBuyer - £69.91
This motherboad has AM3, PCIe 2.0 and a 710 SouthBridge that supports AMD CPU core unlocking. It's also very cheap compared to others their and Gigabyte is a reliable brand.
or
ASUS M4A785TD-M EVO 785G Socket AM3 DVI VGA HDMI Out 8 Channel Audio MATX eBuyer - £67.88
which is the same board but just by ASUS.
For CPU, I'd need help here, because I'm not sure on which batches are the unlockables, but:
AMD Phenom II X2 550 Black Edition 3.1GHz 6MB L3 Cache Socket AM3 Retail eBuyer - £73.74
Which is a dual core AM3 Phenom 2 with good performance and quite a few people have unlocked (by chance, some unlock, some don't, it's just if you're lucky/blessed) to make a quad core. It is also Black Edition, making it easily overclockable.
or (if you're willing to spend more)
AMD Phenom II X3 710 2.6GHz Socket AM3 6MB L3 Cache Retail eBuyer - £87.11
Same story, but this is a more powerful triple core. It's easily overclockable, and also unlockable (again, by chance if you get a good one) to a quad core.
You will need DDR3 RAM though and unfortunately in this store it's a bit expensive, but the voltage is low and the low timings mean it's fast:
Kingston 4GB (2x2GB) DDR3 1333MHz HyperX Memory Kit CL7 1.5V eBuyer - £92.00
there's also a faster and better OCZ Reaper kit, but only 1 in stock:
OCZ 4GB KIT (2 x 2GB) DDR3 1600Mhz PC3 12800 REAPER SERIES DUAL CHANNEL KIT (7-7-7-24) eBuyer - £91.89
I think that's a pretty decent lineup for someone on a budget, don't you?
You will see a good performance jump from your current system at the minimum cost I could find thus far in your store. If there's other stores you use, let us know.