Is there any mapping between MaxMind's locid and GeoNames id?

I use GeoLite from MaxMind. My real task is to determine CityId in our system by specific IP. In MaxMind I find locid by IP and then use hand-maded table of cross between locid and our CityId. But this cross-table is uncompleted. I found good file of localization from MaxMind where each locid mapped to GeoNames id. GeoNames id it's good for me, but this file is uncompleted. For example, there is no Birmingham in this file. So, has anybody such problem? And if any ways to decide it?

MaxMind's GeoLite2 databases return GeoNames IDs.