If you block up at the bottom as suggested make sure that you leave some form of ventillation about 4 inches up from the hearth. This will prevent damp patches appearing on walls higher up the flue. where it passes through higher rooms. Have the flue swept before you block up. This will lessen any debris likely to fall and why I say put the ventillation in about four inches up so that if anything does fall it will not stop the ventillation from working.