I can't speak for Burma or Pakistan, but a few brief comments about India. This includes Pakistan pre-partition, which is outside the scope of your question, but relevant nonetheless.

The British started divesting from India even before WW2, when it became clear that the Raj's days were numbered. This was made easier by changes in laws which permitted Indians to own larger stakes in Indian industry. Whereas previously British industrialists who wanted to leave could only sell their factories to other Brits or else scrap them, permitting ownership by Indians allowed them to sell their stake to Indians instead.

The flight away from India increased substantially during WW2 when many of them sold off their holdings in India and used the money to open factories in England which were needed for the war effort.

So by the time Independence arrived in 1947, British ownership of Indian industry was already quite low. Commercial interests were indeed maintained, mostly in the form of continuing contracts to buy raw materials from India to export to British factories. But actual British ownership of the mines and farms and lumber forests was much reduced. There were some exceptions, such as tea plantations in Assam and West Bengal which remained under British ownership for quite a while.

During the Dominion period from Independence in 1947 to the adoption of the Indian Constitution in 1950, divestment continued. Nehru had made it clear that India was going to take the path of socialism, and this worried foreign investors. After the Constitution was promulgated in January 1950, India formally became the Socialist Republic of India, and the next year Nehru embarked on the first of his several "5 year plans" modeled after the Soviet system. This involved a huge investment in the public sector, mainly in infrastructure. While foreigners were allowed to own businesses and remit the profits back to their home countries, many of India's largest industries became the domain of the public sector, which means they were legal monopolies. The avenues in which foreign businesses (and the Indian private sector) could compete became progressively narrower.

Contrary to popular belief, India didn't embark on any major nationalization program. The first industries nationalized were the banks, in the 1960's. These were all Indian banks only. Foreign banks were still allowed to retain foreign ownership and do business as usual. But the FERA act in the early 70's reduced the scope for these banks, because foreign exchange came under regulation in an effort to protect Indian currency. They could still take their profits in Rupees, but Rupees were not much in demand in the outside world and were not free floated anyway, their exchange rate being set by the Indian government. It became increasingly difficult to take foreign exchange, specially hard currencies, out of India. The government needed them for the purchase of essential commodities, mainly oil. Many foreign banks closed their Indian offices and moved out in the 70's, but many others remained.

Also in the 70's came the nationalization of a few industries, primarily oil. India viewed them as a strategic asset. Fuel was heavily subsidized by the Indian government throughout the decades since Independence, and the government felt that it needed some insulation from the vagaries of the market.

Another problem for foreign companies, including British ones, was the License Raj. Nehru started it off, but it really became powerful during Indira Gandhi's rule, roughly 1966 to 1980. During this period it was very very difficult to do business in India. Everything required a license - starting a business, expanding your business, buying machinery for your factories, buying land. There were production quotas. If you were a textile manager and wanted to import the latest looms from abroad, you were given permission for a specific number, and if you exceeded that, you were penalized. You were licensed for specific production quotas per machine, and if you worked harder and exceeded your quota, you paid fines.

All of this was run by a complex bureaucracy so that getting any of these licenses required pushing papers through myriad offices, which often took years. It was difficult to be competitive and respond to changing conditions in the world markets, because your response was delayed years by the licensing process. Consequently, investment fled, economic growth stagnated to barely 1-2% above population growth. Per capita incomes barely grew and in some years fell below inflation. This period drove foreign investment almost entirely out of the country. The few foreign firms that still operated in India were collaborations with the government owned public sector, which had special privileges.

Things started changing slowly in the mid 80's, first under Rajiv Gandhi and then picking up during the Janata Dal rule of VP Singh. But it was very minor. The big push for liberalization only came in the 90's after the credit crunch when India ran out of foreign exchange to buy oil, and had to hock 60 tons of Indian gold in German and French banks to get an IMF loan to tide them over. This started the period of reforms under PV Narasimha Rao, greatly accelerated under Atal Bihari Vajpayee. License Raj was abolished, the Rupee was floated in the currency markets, limitations on foreign ownership were abolished. Some of the big public sector industries were sold off to private hands, though this was (and still is) a slow process, meeting severe resistance from labor unions.

So the mid 90's is roughly when the Indian economy takes off, as you can see in their GDP growth charts. This is also when foreign companies return to India in a big way.