Look on the bright side and make no mistake - a new PSU was needed for that 7950 as it did not provide anything near 750W as far as powering the GPU and CPU are concerned. More like 408W (my guess 22 + 12 amps max combined output), and it was 5 years old so with degradation common to all PSUs, more so budget ones, it was surely providing less by now. It also lacked a second PCI-E cable for the 7950. And now you have a far safer unit less likely to go boom due to the greater power requirement.
GPU may indeed have a fault that didn't come up during OcUK's testing (possible). Similar thing can happen with RAM and second-hand sales of the same. The seller may have the RAM working perfectly in their system, and then it fails to work/crashes on the buyer's system because their different system (or usage) is exposing a flaw that the previous system (or usage) did not. OcUK apologized for the team handling your case not doing more to help you and just returning the same card after it passed their tests. They offered you a great deal on your new PSU. And you have Bailey's offer of a new card on the table. Hopefully you'll have posted in Customer Service forum too, to make sure they are updated.
Now, until you try the new card to see, it also remains possible that the problem may lie somewhere else, despite the old GPU working fine on your rig. Motherboard maybe. It may not like/may be interfering with the 7950 in some way that does not affect the old GPU. Apart from the PSU's GPU power connectors, the motherboard also provides a bit of power to the GPU through the PCI-E slot. It may not be providing all that the more powerful 7950 needs, or may not be stable enough. Testing with the replacement card first will determine this, one way or another.
I don't know if you have flashed the BIOS of the motherboard to latest version, Trebz. If you haven't, that is surely worth a try. If you can tell us which AMD Gigabyte model it is (CPU-Z will do it), I'm sure someone will guide you through the process if you need any assistance.
Fingers crossed it gets sorted soon and you're a happy duck again.