I did some hopefully-not-too-creepy sleuthing, but starting with your birth index record it was relatively straightforward to establish your mother's name, her marriage, and find her birth record.
In the GRO Index (free account required):
Turning to the 1939 Register shows your mother living with her parents in Stepney. The index shows the following people in your mother's household (I recommend you take a look at the original image):
On FreeBMD you can locate Jacob Rosenthal's marriage to Elizabeth Nerden in 1894 in Mile End Old Town district:
The 1939 Register gives Jacob's date of birth as 6 Jan 1873. This leads back to his likely birth record in the GRO Index:
And most likely his death in 1949, a year later than you expected:
Now, where does the name Newman fit into this? He shows up in a number of London directories and electoral rolls as Newman Jacob Rosenthal. For example, this 1922 electoral roll in Mile End Old Town:
I don't have a good answer as to where the name Newman fits in, but it does not appear to be his birth name. Perhaps it could be as simple as he just did not like Jacob, and preferred to go by Newman.
In any case, it is a relatively straightforward matter to trace Jacob (Newman) through the censuses, so I won't include them all here. Let us know if you have trouble locating him.
The above records are all just index records. I would strongly recommend you start with a few birth, marriage, and death certificates to establish facts. It would be good to start with your mother's birth certificate, so see how her father's name is recorded, and then possibly her father's birth and death certificates. You can order these certificates directly from the GRO Index website.