Unless the builder/NHBC give you a programme of works for each defect and their reasoning, you could end up putting up with lots of "muck and bullets" (aka inconvenience) and even then it may not even solve the issue(s)
At least now there is a recognition of an issue. Pity they intend to ignore the cracked tiled floor properly at the same time.
You are not pushing your luck. It is your home and it is defective and they or NHBC have an obligation to do the works properly.
