I am a doctor in a mental health setting. I am just stating things plainly here. I do not prescribe Diazepam ever. In one year in the community setting I saw it prescribed once in the context of managing withdrawal from alcohol. You have incorrectly stated they cause seizures-they treat seizures by reducing brain excitability, and hence are used in alcohol withdrawal settings.
It is not used as a treatment for anxiety any longer-it is effectively a sedative and not a productive treatment, as well as ( as per what others have documented) causing addiction and tolerance problems. When patients are very agitated or aggressive in the inpatient setting Lorazepam is used as a sedative as it is more short-acting. For anxiety in the inpatient psychiatric ward setting we would prescribe promethazine which is a drowsy antihistamine-you could ask your GP about this as an option.
The only patients I know taking Diazepam have been taking it for years and hence it is extremely difficult to withdraw them, or they have such a severe anxiety/panic disorder +/- PTSD that it has been prescribed short term to facilitate psychological therapies.
If you have anxiety as you state which is above and beyond what would be considered a normal response to a stressful life event then you have an anxiety disorder and treatment is indicated. That means as the GP correctly stated, an anti-depressant. There are various antidepressants with anxiolytic effects. I know you have tried sertraline with poor side effects; you could try a different SSRI drug or there are different classes of drugs. There are venlafaxine & duloxetine which work slightly differently. Pregabalin, which is licensed for pain, is a very effective anxiolytic;it is far less addictive though it still has some street value.
The guidelines do indeed recommend CBT; I know you said you tried this however did you do the homework and are you regularly practicing the techniques? It requires motivation, engagement and to be honest a bit of work, as it is 're-training' your brain. Talking alone won't do it. If you have really tried and found it ineffective then you can ask to be referred for a more intense psychological therapy.
Although there is an element of discretion for GP's their prescribing practices are audited and their arses would be handed to them on a plate if they prescribed in the way you describe. It is far less dangerous for you to have a four week course than use as and when. It introduces so many variables of risk- you state upthread that you took two tablets in one morning which is a double dose. The half life of Diazepam is very long, it stays in your system for days, so when you took 3 in under 24 hours you effectively triple dosed.
I really must hasten to add; don't buy it off the street. Even for personal use this can earn a maximum sentence of two years in prison. I have seen a teenage girl put into a coma by taking what she thought was Diazepam-god knows what it was cut with but thankfully she did make a full recovery.