Ferrite transformer at mains frequency
It is fully possible, but you will need a lot of turns to keep the peak flux density below saturation. Because of this, you will quickly run out of winding area. This in turn will call for angel-hair thin wire to make it fit. Thus high resistance and losses. Use \$ U_{rms}=4.44 \cdot f \cdot N \cdot A \cdot B \$. With ferrite, B would be in the 0.3 T range. A normal laminated iron transformer would go to about 1.2 T and give you a better core-voltage-turn-to-winding-area-ratio for 50-60 Hz. 

Also, think about Al for the core and your number of primary turns. I'm sure it's possible to supply the magnetizing inductance, but that current times your primary resistance will determine your static loss for the transformer.