I don't intend to repeat what everyone has already mentioned, however I'll post it clearly and account for other factors too.
Your entire system is quite old to be honest. If you upgrade the GPU to a GTX 760, your existing CPU and RAM will bottleneck the GPU (hold the performance of the GPU back). So if you upgrade the GPU, you may not notice a major difference in performance due to the weaker components (motherboard, CPU and RAM) restricting your system. If you are planning on playing modern games indeed an upgrade is necessary, as mentioned your system would now be considered obsolete.
The GTX 760 requires a 500W power supply (PSU) with 2x6-pin connectors. Assuming due to the age of your system, your current power supply may not have 2x6-pin connectors hence you maybe required to purchase molex to 6-pin adapters. With that said, your current PSU may not be produced from a decent manufacturer or 500W hence you could require a PSU upgrade too unfortunately.
You may require a new power supply (PSU) to support the GTX 760. Your existing CPU and RAM will bottleneck the GTX 760, hence upgrading the CPU and RAM is ideal first. Upgrading the CPU requires a new motherboard, due to your existing LGA 775 socket now being obsolete (no longer supported/end of life). Intel introduces a socket almost every 2 years, we're currently on socket 1150. The current socket only supports DDR3 RAM, you currently have DDR2 hence will require new RAM. Furthermore your current motherboard supports SATA and PATA/IDE; if you have any drives utilising PATA/IDE, you'll need to purchase new drives unless you already have SATA drives. (You should be using SATA anyway due to it providing better performance over PATA, hence being the successor to the now obsolete PATA.)
To conclude in order to upgrade your could require a new: PSU, motherboard, CPU, RAM and drives (hard/optical disk drives and/or solid state drives). If you wanted you could create a new computer all together, however that may not be possible with your set budget. Regardless if you want to upgrade your existing system with £180, I would recommend the following:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Pentium G3220 3.0GHz Dual-Core Processor (£38.10 @ Aria PC)
Motherboard: ASRock H87M Pro4 Micro ATX LGA1150 Motherboard (£56.09 @ Amazon UK)
Memory: Corsair XMS3 4GB (1 x 4GB) DDR3-1600 Memory (£28.99 @ Amazon UK)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply (£46.93 @ CCL Computers)
Total: £170.11
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-08-06 18:46 BST+0100
The above components are solid to get you started. The 550W PSU should allow you to upgrade to a better GPU in the future, the motherboard will allow you to accept Intel Core i3, i5 and i7 processors and up to 32GB RAM if you ever want to upgrade further (8GB RAM is more than enough for most, if not all gamers anyhow). Don't get it wrong, this Intel Pentium is a new Pentium based on the Haswell architecture and packs a huge performance gain over your existing system. I have not included a graphics card due to your budget, however the integrated graphics of the Intel Pentium is almost similar in performance to your GeForce 7900 GT; hence I would use the integrated graphics until you can save up more funds and purchase a dedicated GPU.
I have also not included any new hard drives or optical disc drives, assuming you already have them in SATA. If your existing drives are in PATA, you'll need to purchase new drives in SATA.
UPDATE:
SubZeroFlsh :
Ok, would it be sensible to upgrade the motherboard, fit it, then save up for the processor and so on...
No. If you purchase a new motherboard your existing CPU or RAM will not be compatible; hence your system will not function. Your current processor is on socket 775, a new motherboard would be on socket 1150; your socket 775 CPU is not compatible with a 1150 motherboard. Only CPU's designed for socket 1150 are compatible.
775 denotes that there are 775 (seven-hundred and seventy-five) pins the processor should connect to on the motherboard; your current CPU only has 775 connectors. The new socket requires 1150 connectors/pins.
Hence your existing CPU is not compatible with any other socket, not even a new 1150 motherboard. Motherboards are not backwards or forward compatible with CPUs.
A new motherboard would also require DDR3 RAM, you currently have DDR2. Then you need to consider your drives, SATA v PATA. If you want more details on this, read my entire post from the start. I personally believe it's ideal for you to upgrade the PSU, motherboard, CPU, and RAM now then save up for your other parts (that way you can slowly upgrade); unless you're planning to build an entirely new system.
All the best.