On which date was the announcement formally made that India and Pakistan would be made free?

The actual division of British India between the two new dominions was accomplished according to what has come to be known as the "3 June Plan" or "Mountbatten Plan". It was announced at a press conference by Mountbatten on 3 June 1947 at 4 pm, when the date of independence of India - 15 August 1947 was also announced.