Would replacing old mortar for new prevent water from seeping through brickwork?
I have included photographs just in case this is a special case:
It wouldn't hurt. looks like a lot of that mortar is just missing with holes and cracks. Looks like rain and a bit of wind could drive rain right through it.
That said, it looks like the brick is also damages. Brick with a damaged face will also take in water like a sponge. They do make spray-on brick sealant. I can't say it it works or not, but might be something to look into.
just looks like the mortar used was not mixed properly- more sand ratio (this is a common problem in British builds form the 1900's)-- and over the years it started to crumble out. In comparison- the bricks are in very good condition compared to the way the mortar crumbled out.. The bricks look solid- I suspect the breaking occurred when you removed the plaster?
Agreed with @Mike Perry - To solve the problem you will need to do it properly- Get the whole palster off, check the state of all the mortar- re point them properly (using sealants..etc) and maybe re-plaster or using some new techniques.. eg insulating it with poly blocks, create will help in heating costs and protects old walls very well. In UK/EU you can go to a .gov site and search for subsidies as the governments can fund up to %50 for insulation and some countries even 100% for green energy solutions..