This problem is totally unrelated to phaser. You only have to stop the the default action from being executed. This is done with event.preventDefault(). You have to add an event listener to the window object. Listen for the keydown event. Check if the key code is one of  the codes for top, down, left, right or spacebar. If so stop the default action with event.preventDefault(). If you want real code to copy & paste in your project use google. Have fun!