From my understanding you need a receipt for a refund if you change your mind, if you don't have one the shop is not obliged to give you your money or a credit note (but they do have to display their refund policy at the point of sale).
However, in your case, the goods are faulty. This is then different. You should be able to exchange them without a receipt, possibly get your money back.
In terms of the bank statement, you could give it a try, but I suspec they won't accept it. That amount of money on that day could have been for anything. In the shops eyes, you could have stolen the trousers and bought something else for the same amount, then when you return the trousers for a cash refund you are making money out of them. I know that is negative, but is likely what they could think.
All of the above is dependent on the type of shop, large multi store chain or small one off shop. All depends really.
Good Luck...