If you're specifically talking consulting prospects in the UK then I might be able to help, but I have no idea how these firms hire in India.
In the UK, you can study any subject and get into consulting, there are no subject requirements. Instead, firms are more selective over the university you attend. For example, the MBB firms mainly hire from Oxford, Cambridge, LSE and LBS. You'd still have a shot from places like Imperial and UCL but most hiring from UK unis come from these four.
Outside of MBB firms, other top strategy and management consulting firms are less selective but still fairly selective with most consultants coming from these unis plus a few more UK ones, top US and Euro institutions. You can just look at employees from these firms on LinkedIn to see where they studied, for example try this this for firms like L.E.K Consulting or Oliver Wyman just to try, you'll see that most come from top UK unis but some come from good but not elite unis.
If you're wanting to work in India for these firms after graduation then I have no idea.