The Flight of the Starling is the story of two test pilots trying out this new warp drive, which allows ships to travel close to the speed of light and finally open the door to interstellar travel.

The plot is straight forward the Starling is launched on its first test-flight, they use the warp drive to accelerate to speeds close to the speed of light, then return to Earth to discover thousands of years have passed in their absence. They land, team up with some future humans, raid a supercomputer defended by some less friendly degenerate future humans, and discover how to put their spaceship into negative space so they travel back in time again. Oh and theres a subplot where the nerdy scientist narrator and nasty bully jock space pilot are vying for the affections of the genius professors shy-yet-pretty niece.

Its an adventure story with a Planet of the Apesesque twist, and extremely of its time. The really meaty bit of the story comes here:

Driven by atomic energy, the generators created a force as the generators of the past created electricity. In some respects the force was electricity, but it was of a higher energy order, containing inherent magnetic properties in a complete union of a kind only vaguely suggested by the term electro-magnetic, in which the two forces involved are more or less mutually exclusive, the one giving rise to the other. The force created in the immediate vicinity of the ship a warp in space a moving warp, which could with fair accuracy be called a ripple in the fabric of space. The ship rode this moving warp or ripple as a surf board rides the moving crest of a wave. The intensity of the force controlled the speed of the warp up to a certain limit.

So we have, from the off, the idea of propelling the ships through a warp in space, created here by powerful electromagnetism.

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Star Trek Didnt Invent the Term Warp Drive, This Sci-Fi Story Did - Den of Geek