Seeking GP support doesn't have to mean a CAMHS referral. You're not equipped to support an anxiety or eating disorder.
I'm wondering if we have done the right thing about reassuring her about use-by dates, perhaps that is feeding her fear?
Honestly, I think it was the opposite of what she needed. It effectively tells her that she is right to be anxious and afraid and that she needs to continue this behaviour to keep herself 'safe'. Thereby keeping her stuck in the cycle.
A more useful action would be to educate her about what sell by dates mean, what use by dates mean - the difference, how they are calculated, why they have to be printed, and most importantly how to make your own safe assessments about food safety.
So, not eating something that is legitimately unsafe (uncooked chicken for instance) based on accurate knowledge of how to assess that is reasonable.
Avoiding eating based on panic and as a way to make the panic go away - not good. That will only cause ever deepening anxiety. That's when she needs support to eat anyway so she can slowly retrain her brain about the boundaries of what is 'safe'.
The brain is risk averse. It very quickly learns new threats - which is why getting your approach right to avoid teaching her brain to be afraid of sell by dates for instance is so important.
It is much slower to relearn that something is safe. So it will take more effort and consistency to help her overcome this anxiety and to be able to feel calm around food than it took for her to get to this level of anxiety.
This is why professional input matters. Not to medicate or label - medication wouldn't help with this, it's coming from her thought patterns - but so that the way you manage it is helpful rather than inadvertently harmful.
The CCI website has a number of free online modules that are often used by the NHS when delivering cognitive behavioural therapy.
I would recommend reading the ones on anxiety (and maybe look through the resources to see if the ones on panic or other areas might be useful too).
It will help you understand what is going on in her brain to cause this behaviour and keep it going, and it will help you to ensure that you stop feeding and perpetuating it but can start helping her bring it back under control.
The basic principle though is not to validate the anxiety by joining in with her behaviours around dates and avoidance but prove she can survive the anxiety-provoking situations instead and help her think about it differently.
Avoid avoidance basically! The CCI site also has good information on how to do 'exposure' therapy type activities in a safe and successful way without overloading or causing more harm.
www.cci.health.wa.gov.au/Resources/Looking-After-Yourself/Anxiety