I am reading a book by C.J. Sansom called Dark Fire. In the book, there is a description of 1540's English criminal justice system.

"When she is brought into court, she will be asked to plead guilty or not guilty. If she refuses the under the law she cannot be tried by a jury. But the alternative is worse.......She will be taken to a cell in Newgate and laid in chains on the floor. The will put a big, sharp stone under her back and a board on top of her. .........Each day more weights will be added to the board until she talks or dies of suffocation from the PRESS of the weight...........Some brave souls refuse to plead and allow themselves to be PRESSED to death because if there is no actual finding of guilt one's property is not forfeit to the State."

I am wondering whether the expression we use today is originated from this torture.

That makes interesting reading but I am not sure.
I did find the following:
Definition of prefer charges

You can also look through the Etymology Dictionary and find charge and press. The word charge - c.1225, from O.Fr. Chargier "load, burden," from L.L. carricare "to load a wagon, cart," from L. carrus "wagon.

So there is a possibility.