Translate latitude and longitude in X, Y coordinates

I have to translate latitude an开发者_JAVA百科d longitude coordinates on X, Y plan. I have decided to use UTM as projection system. I use this page ( http://www.uwgb.edu/dutchs/usefuldata/ConvertUTMNoOZ.HTM ) to test and quickly get result. As test I wann plot on plan London and Rome. Rome has Latitude: 41.90 and Longitude: 12.48. London has Latitude: 51.50 and Longitude -0.12 expressed in degrees.

Using WGS84 and page reported first i've calculated Rome as Easting: 290965 and Northing: 4641744 London has Easting: 699889 and Northing: 5709362.

If I intend northing as the Y coordinate and easting as X coordinata Rome will be western than London and this is a huge mistake (don't you think?)

Where I wrong?

UTM is based on more than just easting and northing, there is also the base reference grid from which the E and N are measured. London and Rome are in different grids.