Fitting a new habitation internal door lock

Having just managed to solve the problem with the door that would not open and thanks to the service center who told me I had to use brute force to get the door open, I broke the door handle from the outside. The outer handle is connected to the inner lock by a rod and within the mechanics of the inner lock, is a piece of plastic that the rod connects to. That is where it broke!! It took ages to get the very fragile plastic internal door covers off and I am hoping to be able to patch up the cracks. I have ordered a new lock, but wonder if anybody has ever attempted this most fiddly of jobs?

I am pleased to advise that I have now fitted the new lock having removed and installed it at least 5 times!! I think I am now an expert on the subject. The reason for the number of attempts was because one of the links (The one that comes from the external door handle key lock) had to have a larger space than I was assuming, and because I was allowing a smaller space meant that everything worked fine except the key lock. I hope I made myself clear!!