We have an end-of-terrace house built around 1895 with solid 9" brick walls. We recently removed the plaster from our living room walls. Most of the brickwork is in good shape but there is a small section (about 1 meter x 1 meter in size) which is in a terrible state. In the worse patch, the bricks can be pulled out by hand. There is also evidence that some of the "header" bricks (i.e. the bricks which span the width of the wall) have sheered in half. I suspect that this area of wall has suffered from two problems: 1) damp and 2) some sort of mechanical stress which has caused the bricks to break up a bit.
It's important to note that the bricks which form the external "layer" of the solid wall seem to be in good shape - it's just the bricks on the internal layer which are in a bad way.
Can I just carefully replace the bricks (using lime-based mortar) or should I call in professionals to rebuild the wall?
You could repair the bricks; one at a time. That way the whole wall can't crumble on you. Only remove one brick, clean out the soft mortar, put in new mortar, replace the brick and go on to the next.