You really do need to factor in a new PSU as well, upgrading your CPU and Mobo won't do you any good if the PSU can't handle the load. You'll just fry your current PSU and possibly damage the parts and brick your computer.
Sorry, but there's no cheap way to solve your problem. A 660 is made to work with modern AM3 GPUs, anything that will fit into an Fm1 slot is going to bottleneck. It might improve performance a little to upgrade to another FM1 chip, but you'll still not be able to get the most out of your GPU.
The good news is that you could split the cost by upgrading the PSU and then upgrading the CPU and Mobo together. Well, you could buy them separately, but the CPU and Mobo have to be installed together because your FM1 won't work in an AM3 slot. FM1 chips are actually APUs, which is a CPU with an integrated GPU. It's not very good for games at all and any FM1 CPU will bottleneck a nice card like a 660.
Honestly, you're probably looking at around a 350 ballpark figure for all three parts, if you go the absolute cheapest, bare bones, but adequate route. You don't need to drop the cash all at once and can buy them one at a time over a period of time. 100 for the mobo, 100 for the PSU, and 150 for the CPU. Parts tend to cost more in the UK so I'm giving a slightly higher estimate here.
You might be able to pull it off on a little over 200 UK if you're careful and shop for good deals. Just make sure the specs match up to what you want and make sure there's enough USB ports to and other connections to suit your needs. You should be fine with 4-6 USB 2.0 ports for a bare bones gaming rig, most any other port you might need is pretty much standard on any Mobo.
Stick with AMD if you're on a budget like that, Intel is nice, but it's also more expensive. AMD will do the job just fine and won't hurt your wallet as much. You want an AM3 Mobo with at least 1 PCIe x16 slot. Unless you also want to buy more RAM you need to also make sure the Mobo is compatible with your current RAM frequency, 2400(OC)/1866/1600/1333/1066 is what current board supports all of these so I couldn't say what you have.
Edit: You should also remember that RAM is cheap, so it may actually be slightly cheaper to get a less expensive Mobo that isn't compatible with your RAM but has all the other features you need and just buy new RAM to go with it.