The original enquirer hasn't been online for over 2 years but, just to confirm for those interested in this school (from Cliff Webb’s An Index of London Schools and their Records, 3rd edn, 2007):
Virginia Road School, Shoreditch High Street, E2. Opened 1875; formerly New Castle Street School; renamed Virginia Primary School, 1951.
LMA has (under EO/DIV 5/VIR):
Admission/Discharge: 1875-1928 (boys); 1875-1939 (infants); 1902-1930 (girls)
Logbooks: 1900-1943 (infants); 1913-1929 (boys); 1914-1930 (girls); 1939-1943 (mixed)
You’ll find some of the A&D registers (up to 1911) on Ancestry, but not the later ones, and not the logbooks of course.
Closure for school records at LMA is 65 years from the last entry (except for A&D registers, which are 30 years). So all the above should be open to access.