apply new born baby Indian Passport

Hi,
I am on Tier 2 general visa ....My baby has born in london...and we had moved to Leeds when she was 2 months old.Now need to apply passport for her in Birmingham.She got her council birth registration at london....so here my doubt is shall we apply her Indian Embassy issued Birth registration at Birmingham? or should apply at London........If so do we need to apply in person?or by post?....and for the passport where do we need to apply?(birmingham or london)