Interviewing for K-1 in London

[MARM 7]

We needed some advice regarding the following, if anyone knows anything about this...

My fiance is interviewing at the US Embassy in London for his K-1 visa. His Pakistani passport is currently with the UK Border Agency because he recently had to apply for an extension for his UK student visa (on which he has been in the UK for the past few years, which is why he is interviewing in London). In order to get back his passport in time for the interview, he will have to call the UK Border Agency and ask for his passport back, in which case his application to extend his UK student visa will be automatically withdrawn. He will apply in London for his K-1 and go to the interview WITHOUT an extension on his UK visa, but WITH his Pakistani passport (and a letter from the UK Border Agency explaining he withdrew his application for extension for his student visa). Will this mean that he cannot get interview for his K-1 visa in London? Because according to the UK Border Agency, he should be leaving ASAP after withdrawing his UK student visa extension application.

We are worried about whether he will still be eligible to interview and successfully receive his K-1 visa through the embassy in London after withdrawing his UK student visa extension application.

We have already emailed the US Embassy in London and the UK Border Agency regarding this issue, but were looking for any advice from people here on VJ as well. And, we have already postponed the interview date, so that option is not valid and is out of question.