Certainly your employer can advertise a vacancy as being full time if they think those are the hours required to do the job, there's nothing wrong with them doing that. They've obviously had some discussion at some point about what hours are required for this post and decided they need full time hours.
Even if they won't consider external candidates at present, perhaps they are confident that there will be someone suitable internally who is prepared to do the hours required.
It does seem a bit shortsighted of them I agree, but in the current economic climate, there is a lot less motivation for employers to be flexible to accommmodate candidates. As your employer won't consider external at the moment, obviously there is a greater chance that they won't find someone suitable internally and might then be prepared to reconsider.
You can put in a flexible working request, but only one a year. So assuming you haven't put in a request in the last year, you could apply for the job on a full time basis, then, once you are in it and performing successfully, you will be in a position to put in a request and demonstrate clearly and realistically how the job could be managed on less hours.
Have you put together a 'case' explaining why and how you think this new job could be successfully managed in less hours? I would suggest you do so if you haven't anyway. If there are financial concerns where you work, the prospect of a significant salary saving by having a part timer rather than a full timer could be emphasised.