I have a Radeon HD 5770 paired with a Phenom II X4 955, and it games pretty well at 1920x1080 on med/high video settings.
I would check out "Best Graphic Cards for the Money - December 2011" on Tom's Hardware's main site to see hierarchy-wise where your card sits now and what budget-wise you'd be looking at for at upgrade.
Don't know if that's much help from me, but that series of articles is a monthly tome to component upgrades, from video cards to processors.
Your in a difficult position here. Personally I would always go with a GPU upgrade first, restrictions(bottlenecks) can occur but most of the time you will see a decent amount of improvement if not all the performance the card is capable of.
the problem you have is you really need a 6850 at least to make a decent upgrade. Im pretty sure your GPU will restrict that card so you really need a CPU upgrade as well.
The 6850 is about £110-£115 although I'm sure shopping around could shave a bit off.
The CPU, well you would want a Quad I would think ? and a decent Phenom II type CPU like a 955/965 or even a 960T will cost about £90- £100.