Sanskrit is Indo-European, as is Latin, Greek, German, Tocharian, etc.
Much of the argument for claiming a more ancient origin for Sanskrit is based on a hijacking of Dravidian tradition.
BTW, Sumerian is considered to be a "close relative" of the Dravidian group, but not exactly a cognate of any extant Dravidian language. The Sa'ami languages are also more closely related to Sumerian than to the so-called Fenno-Ugric group (which still provides a lot of vocabulary to the Sa'ami languages but not the grammar).
Whatever the Brits thought is irrelevant. They have the same problem ~ they're stuck within the more primitive and less ancient Indo-European language group using borrowed alphabets.
The whole “Aryan invasion” thing was made up and is not factual. I accept Vedas and if historians agree with Vedas, fine. If they contradict them, I don’t agree with the historians.
People can argue historical details but as a student and follower of the Vedas, I accept them as infallible and truthful.
Stephen Knapp’s website has a lot of historical evdidence (and tons of other stuff, it’s a rather confusing website), if you’re interested. I find it hard to navigate but he used to have some links to interesting historical info.