In my opinion, it's that they saved the blues as a distinct and popular musical genre.
In the beginning, there was Elvis. And others, yeah, but Elvis is the "big name" of early American rock'n'roll. His debt to the blues was obvious early on. But his music swiftly started merging back into the pre-rock'n'roll "mainstream pop" area in lots of ways.
But over in England, people like Eric Clapton and Keith Richards and Jimmy Page and a bunch of others were all about the blues. And they became big enough names that they were able keep Muddy Waters and Howlin' Wolf and Robert Johnson looming large in our collective memory and help blues-verging-into-rock'n'roll musicians who were popular but treated suspiciously because of their skin color and might otherwise have faded -- the two that come immediately to mind are Chuck Berry and Bo Diddley -- remain "relevant."
No, I'm not saying I don't love me some of the pop-ish (and later, psychedelic) British Invasion music, and that those guys didn't do some damn good stuff that was all their own. But if I was only allowed to give them credit for one thing, it would be for introducing me to the blues. If not for them, I'm not sure anyone else would have done so.