Every so often, I get a PM from someone who has searched for Wellbutrin and found that I've managed to be prescribed it. So, here is my comprehensive answer for other enterprising searchers (not that I mind being PM'd, I just forget about them sometimes).
I don't want to go into any sort of great detail about my mental health here, but I will try to explain enough to make sense.
I've been on Wellbutrin (buproprion), Lamictal (lamotragine), and Zoloft (sertraline) for going on 3 years. Suffice it to say that I am suffering from depression in conjunction with other anxiety-based problems.
I went to my GP who balked at the number of meds I was taking and what kinds (for both Wellbutrin and Lamictal). He said he could not prescribe the medications without being told it was okay by a psychiatrist. He told me that as he couldn't prescribe them, and that as it would take a lifetime to make it through the mental health system and that I would have long since run out of meds, he would recommend me to a private psychiatrist.
He did. I went to a doctor at the Priory. It cost £150ish. The psychiatrist at the Priory prescribed the meds. They cost £150ish.
I then switched GPs because I didn't feel comfortable with the first one and found a great and sympathetic GP who has helped me to no end. She was able to keep prescribing the medication under the Priory guy's instruction.
I then entered the "mental health queue". I did the intake interview, which was awful. The doctor was rude, preoccupied, and didn't listen to me. She had no experience with my conditions. I went to my GP and discussed everything with her. We decided a plan, together, that is appropriate. She worked with the intake doctor and I'm now on track to be seen by a specialist.
I appreciate the NHS. Of course they don't have the time and resources that my $300/hour dr in the US did. That doesn't mean that I haven't been my own advocate and fought for what I need. Mental health is a delicate area.
I stress that I have a long and in depth history that contributes to my inability to change meds quickly or without support (not that anyone can do either, but I have some particualr issues). I stress that Wellbutrin is NOT prescribed here to treat depression. I stress that I seem to be an anomaly. I also stress that when it comes to your mental health, make sure that you find someone you're comfortable with and work together. If you're dissatisfied, be prepared to stand up for yourself but also be prepared to work with the system. Private care is expensive but the NHS can be slow.
Basically, it's not impossible to get Wellbutrin, but it's close to impossible. I hope this helps someone, even if it's just travelling the long path of the mental health system here. I also hope I've been clear enough about my situation, but if this is confusing, I'll try to clarify. Good luck to everyone.