Convert GPS coordinates to Web Mercator EPSG:3857 using python/pyproj

from pyproj import Proj, transform
print(transform(Proj(init='epsg:4326'), Proj(init='epsg:3857'), -0.1285907, 51.50809))  # longitude first, latitude second.
# output (meters east of 0, meters north of 0): (-14314.651244750548, 6711665.883938471)

The "trick" is to use these shortcuts for Web Mercator (EPSG 3857) and WGS 84 longitude and latitude (EPSG 4326). The init key means "initialize this projection by reading the definition for 3857 from the 'epsg' file."