This is a government report into the effect of month of birth and academic attainment. I've copied and pasted some of the key findings:
At Key Stage 1 in 2009, the gap in the percentage of pupils achieving the
expected level between summer and Autumn born pupils stood at 10 percentage points for writing, 8 percentage points for reading, and 7 percentage points for maths
Key Stage 2 - The gap between summer and autumn-born pupils in achieving the expected level for English and maths is 8 percentage points. Just 43% of August-born FSM boys achieve level 4 in English and maths
compared with 84% of September-born non-FSM girls.
GCSE attainment is used to assess the overall achievement of pupils at the end of Key Stage 4 (typically age 15). The following analysis presents the term of birth and month of birth gaps in achieving 5 or more grades A*-C at GCSE (“five good GCSEs”) including English and maths. The gap between summer-born and autumn-born pupils stands at 6 percentage points. (47% of August births got 5 A to C GCSEs including English and maths, compared to 55% of September births.)
Of those students from the maintained sector KS4 cohort of 2007 who entered for Key Stage 5 qualifications (by any route) by 2009, September-born students averaged 21 QCA points more than those born in August, where 30 points = 1 A-Level Grade.
Autumn-born young people are more likely to enter for three or more A-levels than those born in summer (Fig. 2.2a). This feeds through into a 4 percentage point gap in the proportion entering for two or more A-levels (giving them access to Higher Education) between those born in August and September.
See also this news report on month of birth and how it effects entry to Oxbridge.
There are of course other factors that contribute to academic success, but month of birth seems to have a lasting effect throughout education.