There were 3 old numbering systems in use prior to 1950.
First, prior to 1920 each regiment had its own system of regimental numbers (each starting at 1). If a soldier transferred to another regiment he got a new number.
The second system was introduced in 1920 under Army Order 388 with each regiment allocated its own block of numbers:
Under this 2nd block of 7 & low 8 digit numbers the RAOC were allocated:
7574001 - 7657000 and 10530001 - 10600000.
The third system was introduced during WW2.
These 8 digit numbers were allocated in blocks in the 14xxxxxx, 16xxxxxx and 19xxxxxx series.
It was this process that was rationalised into the 1950-2007 numbering system
Ref
http://www.arrse.co.uk/wiki/Army_number
So with a 1918 Pattern RAOC Badge which only started to be issued in 1919 and a low Block 2 Number it is safe to say its from the 1920's but nothing further than that.