The Balkan Plan for fragmentation of India was an idea proposed during the period of Indian Independence. The options given are notable figures of that time, so let`s dissect each of them:

Option 1: Winston Churchill was a British politician and Prime Minister during World War II. He was not directly associated with the Balkan Plan which aimed at the fragmentation of India.

Option 2: M. A. Jinnah was a key leader in the creation of Pakistan, but the Balkan Plan, which aimed to fragment India into smaller states as in the Balkan Peninsula, was not his idea.

Option 3: Lord Mountbatten was the last British Viceroy and first Governor-General of independent India. He was the one behind the Balkan Plan. His initial plan was to maintain India`s unity, but as the communal violence increased, he proposed the balkanization of India, a plan later abandoned.

Option 4: V. P. Menon was an Indian civil servant and played a crucial role in India`s independence. However, he was not connected with the creation of the balkanization plan.

Hence, the correct answer is Lord Mountbatten (option 3).