I am not familiar with the Birmingham consulate but I believe they are all the same. They have specific days and times for issuing visas and you leave your passport and application until the afternoon when you collect the outcome - that is unless there has been a change recently.
I thought they didnt do that anymore, that you had to use an agency of their choice or have I been misinformed I was told you can no longer go to the Indian Embassy in London and get a same day visa and if it applies to London must also be the same for Birmingham ?
It may be a bit late in answering your question, but I go to B'ham visa office ,and now you go with all the docments and leave until a pre-set day for collection.If urgent try the postal services....