A beast would be next to impossible for £500. I think the most you could hope for is loud dog.
At any rate, your system is not really that bad on the graphics card front other than it is only Direct x 10.1. It is also only slightly less powerful overall than the Ebay machine which would be a decent deal for someone who does not build.
In the case of your CPU, improvement would be well within the budget. Right now the defacto budget CPU is the Intel Core i3-2100. I have one and it is amazing. At stock speed, it is as fast for gaming as anything AMD makes.
For the video card, you would need to go up to at least the 6870 level to see a significant difference. It burns slightly more power than the 4850, so a PSU upgrade might be in order as well. You can get a decent Novatech Black unit for ~£50-60. This is assuming you have not already upgraded the PSU as the300w stock one on the HP should have had trouble running the 4850 card.
Assuming you have 64 bit Windows, bumping up to 8gb ram would be a nice boost as well.
At any rate, what I would suggest for now is the i3-2100 and a decent Gigabyte or ASUS P67 or even z-68 motherboard. These are the most modern, and will allow for a better upgrade path down the road. They needn't be the expensive models either. The lower end uATX boards will do just fine. Most will even do dual graphics cards these days if desired.
Tom's has a Graphics Card Hierarchy Chart that lays out the current cards in tiers according to gaming performance. You have to scroll down to see your original 8600 GT, so the move to HD 4850 was a smart one. I'd say it's time to upgrade again. I would get a DX11 card a couple of tiers up just to see whether that wouldn't float my boat. Your processor and mobo are relics, to be sure, but most of the graphics power is in the card, and you can always use it in your new build (the one you will start saving up for right now) if it doesn't improve your experience enough in your HP. Don't get me wrong, you do need a new rig, it's just that If you build one on a 500-pound budget (786 USD), you will be spending on many things that will have no effect on gaming performance, and you will have to skimp on the graphics card.
For 500 pounds you can get a lot of card; you wouldn't have to spend it all by any means. This is all supposing that an HD 6950 or 6970 or a GTX 560 Ti or 570 would physically fit in the HP. You would also need a bigger power supply---exactly how big the card manufacturer will tell you.