Actually you don't have a right to an ELCS. Its a common misconception, but an important one to understand. You can not just go and demand a CS and be guaranteed to get one.
However, you do have the right to the most appropriate care for your personal circumstances - and this may well include having an ELCS.
The subject is rather conversational on the whole, and there are still many within the profession who are opposed to ELCS on certain grounds. You may well face opposition and be told that you 'have no chance' of being granted one. I do believe that a lot of this attitude is about putting off as many women as possible before they explore this avenue fully.
The good news is that the NICE guidelines are favourable to women who are extremely anxious over having a VB. They backup the idea that mental health reasons for an ELCS are as valid as physical reasons for an ELCS.
They outline a process for women in your situation, which has been interpreted in a variety of ways, but in essence the idea is that you should be offered counselling and the opportunity to discuss your fears, but if after this, you are still not happy with the idea of a VB, you should be granted a CS. If the consultant you are seeing doesn't want to do this, they should refer you to someone who will. The underlying principle is that diagnosis of women who really need an ELCS on mental health grounds is an incredibly subjective thing, and in the pass this led to some women being actively forced to have a VB. The NICE guidelines felt this was extremely unacceptable, because they felt that denying a woman access to an ELCS could in fact be even more damaging to a woman's mental health, so on balance decided that it was better to support women wanting one.
The bad news is no one is obliged to follow the NICE guidelines; they are only guidelines. This has lead to very little consistency within the NHS about understanding and support for the issue unfortunately. Some Trusts are incredibly proactive and supportive. Others are not. There are even a couple who have imposed 'blanket bans' on maternal requests, and extend this to women in your situation. Fortunately they are small in number. And from all the threads I've seen on the subject on MN I've only seen a couple who have ultimately been denied if you are prepared to fight and understand it can be a stressful process.
Having said all that, there is something of a movement of encouraging women in your situation to have an ELCS for trauma, and actually this might not actually be the right thing in your personal circumstances. I think this is important to stress, and perhaps encourage you not go in all guns blazing, but to listen to them as much as they listen to you.
I am very fortunate in that the hospital I have been attending, is supportive of ELCS for mental health, but understand that actually, what the best option is, is to build a relationship with a woman, and fully understand the individual elements of her fear. They have a lot of woman who ask for an ELCS who after being given alternatives that are acceptable to them, and being put in a position where they feel in control, actually do change their minds without pressure to do so. But they are also fully supportive if you still want to have an ELCS.
This is why I say that it is important to fully explore your previous birth experience and to discuss how you feel, as ultimately, most women who ask for an ELCS tend to be united by one thing; they need extra support and reassurance regardless of how they ultimately give birth. ELCS are not the only solution to this problem - they are just one option. There is NO RIGHT ANSWER to this issue. Only the right answer for YOU.
As for crying in your consultant appointment... really don't worry about it! If anything, it shows how much this is affecting your mental state. It won't count against you. I would however, encourage you to take someone with you who can help support you and put forward your case and I would recommend you writing as much as you can down before you go to the appointment so you can better articulate how you are feeling and not forget an important point, in case you do go to pieces.
You may be surprised, and despite what your midwife has said, find the process fairly easy. This was my experience (though my circumstances are somewhat different). I was booked in for an ELCS at 16 weeks. You may also find it a real battle and struggle to get an agreement until 36 weeks. I wish I could offer you a better guide as to how it is likely to go, but as I say, there is considerable inconsistency of care throughout the NHS (Despite the NICE guidelines which were intended to stop this, but instead have actually made the situation worse).
Good luck. I hope that you ultimately feel comfortable with your plans for your birth, whether that be an ELCS or a VB.