Hi - I don't think you mean propofol OP, as all that seems to be offered is nothing, sedation using midazolam/fentanyl, both with/without Entonox "as needed" - stuff that's administered by the endoscopist. Propofol and upwards GA needs an anaesthetist present - which is rare for urgent/screening requests.
You can pay privately for propofol I found - but this literally only manages the anxiety for the procedure - you are on your own before and after.
In exceptional circumstances the NHS will provide propofol sedation - but seem to want you to fail a few times with the standard offering first.
As someone that is also phobic - I don't want to attempt it in case it fails - as I think that would make me worse!