Ok. Having done some more google search and splitting hair a little further, here's how I am able to find:
Step 1: Go to http://www.education.gov.uk/schools/performance/
Step 2: Type in the precise post code - let's say B14 7QJ and hit search button adjacent to it
Step 3: You'll be taken to a page listing all schools within the default section of 1 mile
Step 4: Click on the school you are interested to find DfE number for
Step 5: Now, don't be disheartened in not finding the DfE number and only the 6 digit Unique Reference Number. On the right side, you'll find a link to download more information (Download full set of school data CS
V). Then open the Excel file.
Step 6: Approximately, the 4th field in the Excel Sheet will list the 7 digit DfE number