Succession under multiple intestate estates

Hello, I would be grateful for some assistance.

I am instructed by my client on the intestate estates of his grandparents. The only real asset of the estates is the family home, which is in his grandfather’s name.

My client’s grandfather died in 1982 intestate, his immediate family being my client’s grandmother and my client’s mother. The estate was not administered.

My client’s grandmother died in 1996 intestate, her immediate family being my client’s mother. The estate was not administered.

My client’s mother has agreed to renounce title in the estates, which leaves my client as the sole administrator as he has no other siblings.

I therefore need
a) Letters of Administration on my client’s grandfather’s estate and
b) Letters of Administration on my client’s grandmother’s estate
in order for the family home to be in my client’s mother’s name.

I do not believe either estate is liable to inheritance tax but I will check this.

My question is: do I need to go through the whole process of a) before then going through the whole process of b)? Or is there a quicker solution?

Many thanks in advance.