Being honest, you are cutting it fine now at 34 weeks without having previously discussed this with a consultant. You need to take action NOW, and not accept waiting for anything until you have that referral booked.
Please remember that mental health is a health issue and therefore a reason for a CS even though hospital will try not to openly acknowledge that. Mental health can be a 'clinical indication' though how this is defined can differ from hospital to hospital.
Even switching hospitals at this stage could prove difficult as you will have to change everything over and then book an appointment with a consultant which takes time.
You need to get tough and not take no for an answer. If they refuse to discuss the matter, you go over their head and say you are unhappy with how you are being looked after and feel that you are being phobed off and not listened to. You will need to go through the complaints procedure.
Do not take 'this hospital does not do them' as an answer. Its not an acceptable answer, as they are not properly addressing your underlying concerns that are leading to you making this request. This is unacceptable and is a failure of care. They need to do something to relieve those concerns - even if it is to start discussing your birth plan early and give you an alternative plan to help you cope with a VB rather than an ELCS.
This is the angle you need to take rather simply 'I want an ELCS'. They have a duty of care to address your anxiety, whilst you do not not have a right to an ELCS. This may mean that the best way to address your anxiety is to agree to an ELCS, but the point is that failing to act to support you if you are anxious is a breech of your right to the best and most appropriate care for your situation and condition. The difference is subtle but you need to understand the difference and why and how the system works.
The trouble you have here is that having previously had a VB and you yourself say it was not traumatic, you are not really making a case for a CS. Another VB statistically is safer for you and the baby with this in mind - UNLESS there is a mental health reason here. This does mean that they are probably more like you to encourage you to go down the route of a VB with more support / stronger birth plan unless you have a very compelling reason to dispute this.
You need to therefore think carefully about what your grounds are for a CS I feel. Bare in mind that 'traumatic' can mean distressing whilst physically 'textbook'. It is completely in the 'eye of the beholder' in terms of how you and you alone view it. But you need to be able to demonstrate what this actually means, how this is causing you anxiety and to what degree and most importantly have a consultant agree with this assessment.
Realistically, without knowing the ins and outs of your situation and exactly why you want an ELCS you may still struggle to get an ELCS, from what you've said here. Their failure here - and what merits a complaint - is them not listening to you and taking you seriously
It is down to you to be proactive and take control of the situation rather than waiting for someone to listen to you ultimately though.