I seriously doubt you would find AFCO staff who are 'suffering' from the degree of apathy you suggest. After all, they are all subject to a suitability interview and a month long course at RAF Cranwell and any obstructiveness gene in candidates would be picked up there surely before they got to the 'frontline'.
I've never heard of allocation of AFCO depending on postcode. Certainly when I joined up I went to Gloucester CIO even though there were 3 other career offices closer to my home address. Not once was it ever suggested I go to these.
After all, isn't the trick to get you through the door in the first place? Why would you be sent elsewhere? Wouldn't surprise me if each AFCO has a certain quota of enlistments they have to fulfill, so it wouldn't make any sense to send a potential recruit to another office.
Try the RAF 'Flagship' AFCO in St Georges Court in Central London. At the very least you can have a bit of a shop on Oxford Street afterwards or take in a gig at The Astoria (or if its a G.A.Y. night there it might even help on your application form!!
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Good luck, but don't dismiss the staff as obstructive unless you have directly experienced it yourself, in which case help out others by naming and shaming the individual to the OC - after all, we don't need those kind of people in the AFCO's IMHO.
CC