This was claimed by Dr Manmohan Singh in 2005 when he received his honorary degree.
The full quote which I had to truncate:
There is no doubt that our grievance against the British Empire had a sound basis. As the painstaking statistical work of the Cambridge historian Angus Maddison has shown, India’s share of world income collapsed from 22.6% in the year 1700, almost equal to Europe’s share of 23.3% at that time, to as low as 3.8% in 1952.
How much wealthier were precolonial Indians than Britishers?
They were significantly poorer.
Comparing Maddison's data/estimates for UK, Western Europe, all of Europe except Russia, and India for 1700 and 1950, we have:
1700
| Region | Population | GDP | GDP per capita |
|---|---|---|---|
| UK | 9 | 11 | 1250 |
| W. Europe | 81 | 81 | 993 |
| Europe | 100 | 92 | 920 |
| India | 165 | 91 | 550 |
| World | 603 | 371 | 615 |
1950
| Region | Population | GDP | GDP per capita |
|---|---|---|---|
| UK | 50 | 348 | 6939 |
| W. Europe | 306 | 1396 | 4569 |
| Europe | 394 | 1581 | 4013 |
| India | 222 | 359 | 619 |
| World | 2528 | 5336 | 2111 |
where populations are in millions, GDPs are in billions of 1990 international $, and GDP per capita is in international $ (data from the Maddison Project, Maddison's original data). The data are estimates only, but are reasonable estimates. Basic subsistence level is a GDP per capita of 400.
In 1700, India did not have a 1/4 share of the world's economy because Indians were rich, but because India had about 1/4 of the world's population. Most Indians in 1700 were farmers living little above a basic subsistence level (after paying their taxes and/or rent, they would be at close to subsistence level). Britishers of the time were, on average, over twice as wealthy.
According to Maddison's estimate of the Indian economy of 1700, Indians were better off at the end of the colonial period, but not by much - most Indians were still farmers living little above a basic subsistence level. India was still predominantly rural at independence, with an urbanisation rate of 17% (and still only 31% in 2011).
While it can't be correctly said that British colonial rule made India poorer (because Indians, and India as a whole, became richer under British rule), it is fair to say that the British did not promote industrialisation and economic growth in India anywhere near as much as they could have. If we look at economic growth in uncolonised non-Western countries from 1700 to 1950, the GDP per capita of Iran increased from an estimated 600 to 1720, Turkey from 600 to 1623, Thailand from 570 to 817, Nepal from 400 to 496. Despite colonial rule, Sri Lankan GDP per capita increased from 550 to 1253. Very slow growth in some uncolonised countries (e.g., Thailand and Nepal) shows that lack of promotion of industrialisation and economic growth can happen without colonialism. So it's hard to say exactly how much economic impact British colonial rule had on India. It clearly wasn't positive, but it's impossible to quantify.
References:
Maddison Project: https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2020
Original Maddison data: http://www.ggdc.net/maddison/oriindex.htm
While you're waiting for a more recent answer, here's this one from six years ago that clears up some misconceptions regarding that statistic.
A similar question was answered by /u/IconicJester.