The document drawn up by Members of the European Parliament (MEPs) in the EU's influential trade committee points to British Prime Minister Theresa May's stringent visa policy towards Indian professionals as a major stumbling block to the FTA, which has been in the works since 1997.
India's high import tariffs on Scotch whisky from Scotland is seen as another hurdle, which would also no longer be a factor post-Brexit, The Guardian reported.
"In case the UK (including Scotland) would leave the EU, this could possibly facilitate FTA negotiations [for the EU] as tariffs on wines and spirits constitute an obstacle. This as well as financial services, would then become a bit less of an offensive interest of the EU," they add.
The European parliamentarians also suggest that despite the much-hyped India-UK ties, Britain is likely to struggle to clinch a new trade deal.
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They point out that as a trading partner of India, Germany is the top EU country (ranked 6th), whereby the UK figures only rank 18 between Kuwait and Iran as a trading partner for India.
While the UK makes up 3.4 per cent of India's overall exports, it accounts only for less than 2 per cent of India's exports.
In addition, currently the UK has by far the largest trade deficit in goods with India of any EU member states accounting for 2,611 million euros, while Belgium and Germany have a large trade surplus with India.
The MEPs' document, leaked to the newspaper, does however see a threat to the EU's other trade talks in Britain's withdrawal. In particular, there are concerns that the negotiations with Australia and New Zealand due to start in mid-2017 could be scuppered.