If I have been given the proper information (which I am not completely sure about) the one stop appointment includes your bloods being taken as well as seeing the dietician, the surgeon & the anesthetist at Salford Royal/Hope. Your sleep apnea test and psych eval are in different departments and will be scheduled seperately from my understanding. If in doubt ring the department to ask, they should be able to tell you what to expect. I have been told that these clinics are held weekly on Thursdays.
As for the psych eval in general (each case is different so depending on your answers you may be asked different questions) you will be asked about your weight history (what you have tried & failed with), if you understand what you are embarking on and what self-esteem/depression/anxiety issues you might have. They are also going to evaluate what type of support system you have to see if you will need additional support post-op. It is pretty straight forward and it serves you best if you are honest. And everyone gets emotional about their own bodies, experiences and such so don't worry if you cry, they won't judge unfit because of that.
HTH,
Nic
p.s. - I did gain weight between seeing the consultant and seeing the surgeon but nobody ever mentioned it. Unless you have been specifically asked to maintain your weight or to lose x amount of pounds I would think you would be fine.