Do I have to tell US consulate before/after marriage in UK?

I arrived on a "fiance" visa on October 11, and yesterday we just gave notice at the registrar's office to marry in January. The registrar mentioned to me that I might have to notify the US consulate or embassy in London. She wasn't sure, but she says some nationals of some countries do.

Does anyone know if I need to do this before or after getting married in January?

Thanks!

The US and UK recognise marriage in each country.  So no, you don’t notify the US.  You will be legally married everywhere!