Standard stamped iron laminations, core cross section 7.4cm x 3.8cm.
At one Tesla and 50 Hz that works out to about 0.6 volts per turn.
For 240v (240/0.6 = 400) secondary will require 400 turns.
At exactly 12v, each primary half will require 12/0.6 = 20 turns. (40 turns centre tapped}.
But your battery is not going to be at exactly 12 volts, the voltage is going to be all over the place as the battery discharges.
The secondary voltage will be all over the place as well.
But for 12v square wave input, you should get 240v square wave output.