MPs have warned that the UK is "falling behind in the global race to engage with a rising India".
The foreign affairs committee said it is "time to reset" the UK's relationship with India as it gets ready to leave to European Union.
According to their new report, Building Bridges, the committee says that the UK's migration policy "has at times undercut our broader strategic objectives for the relationship".
The report adds: "While the Global Britain strategy is not being heard clearly in India, the 'hostile environment' message is getting through.
"Movement between the UK and India is what builds the living bridge, and students ensure it will remain strong long into the future."
It also said that India's place in the world was "changing fast" and that the UK's strategy "has not yet adjusted to this new reality", adding "we cannot afford to be complacent or rely on historical connections to deliver a modern partnership."
The committee also warns that the UK's efforts to build relations with China "should not be pursued at the expense of ties" with India.
It adds: "There are certain practical steps the Government must take to reset its relationship with India, in particular making it easier for Indians to visit the UK and to work or study here."
The chair of the committee, Conservative MP Tom Tugendhat described India as an "essential partner" to the UK.
He said: "More than a million people of Indian heritage currently live in the UK. Our international interests are guided by similar principles: we have strong links through a diaspora, trade, investment, education, tourism and security interests - and as democracies, we share a strong stake in upholding the rule of law.
"Despite these opportunities, the UK has failed to give the relationship the attention it deserves. We missed an important symbolic opportunity to issue a full apology on the 100th anniversary of the Jallianwala Bagh massacre and recognise wrongs that also punctuate our shared history."
He added: "As new powers challenge the structure of global trade and dispute resolution, we cannot miss the opportunity to partner with India.
"Trade, security, a shared commitment to the rules-based international system - these are all factors in our growing and evolving partnership.
"The Government needs to make sure the UK is making its support for India clear, reawakening the ties between us and building bridges that are made to last."