Well, There are several aspects to this very broad question.

Politically, Indian system mirrors very closely the system of governance of Britain. That is a direct influence of British rule of India. The lower House of Parliament is a literal translation of the “house of commons” - Lok Sabha. The upper house, however is a federal body with state houses nominating members to sit in it. The upper house however - like the House of Lords - is a little weaker than the lower house. Head of state of India is the president who holds similar powers to that of British monarch and performs similar duties. President is not elected directly, but rather appointed by the electoral college.

Educationally, India follows a school education system that the British instituted in India starting 1830s. It has been improved upon by the education commission of India but in essence it mirrors the English education system. The equivalent of GCSE and A levels Exams are conducted after 10th and 12th grade ( junior college) . On the other hand, many schools that were opened in India to educate the royalty still continue to hold the prestigious spot they held during the British era - like Mayo College and Doon school. These are similar to the prestigious “public schools” of England.

Also, the British started the first modern universities in India in 1857 - in Bombay, Kolkata and Chennai( Madras ) which still continue to be prestigious. But other institutions like IIT and IIM founded directly after independence have risen to prominence as well.

Economic impact of British Raj on India is well documented. British rule in India saw India’s share of world economy decline from 18% at the turn of the 19th century to about 3.6% upon independence. The old numbers are estimates of course. But one can at least glean that Indian GDP as a share of world GDP fell significantly over time. This was mainly due to rapid industrialisation of the west which was sluggish in India - due to the policy that favoured British industrialisation.

This meant that India was a mainly rural and agricultural nation upon independence- and still remains as such, though to a lesser extent. Post independence, India followed a socialistic model of development. In this, India looked mainly to russia rather than UK or US for much of post independence history. This further stunted India’s growth and India’s share of world GDP continued to fall as the East Asian countries improved. Since 1990s Indian economy has been liberalised. And situation is improving.

Thus, post independence the main impact of British Raj upon Indian economy - if one wishes to look for one - has been the inherited poverty and undeveloped economy that India continues to struggle with. And post independence policies have not helped.

One more aspect that might be overlooked is in the partition of India and conflicts that have followed. These have meant that India has had to spend a significant amount of annual budget to supply the worlds third largest armed forces by size. In 2017 union budget, Indian military spending consisted of about 15% of the total budget and 2.5% of GDP.

I am sure I am missing some aspects of British Raj’s impact. As it is a broad topic. Any further questions are welcome.