I read this in the early '70s - I'm not sure if it was in a proper anthology, or just an extra story added in to pad out a short novel to proper paperback size.
Set in England (so probably a British author), mysterious globes of energy begin appearing and crushing everything in their path before disappearing again.
The male protagonist gets involved when he narrowly escapes, when the building where he works (possibly a lab of some kind) gets destroyed by one of the globes. Possible that he was in his car at the time - he got out before it was crushed but possibly a female passenger didn't.
On investigating, he finds that the globes contain starships from another dimension - to them our dimension is 'hyperspace' and the globes are how their ship's warp bubble manifest themselves here.
He manages to get inserted in one of the bubbles and contacts the crew of the ship inside - I can't remember how the story ends.
Since posting this I've remembered one more snippet of information. The original globes appeared near London, and were black. Later white globes started to appear in the Midlands - at one point a black globe and a white globe travelled to meet each other. It later transpired the different coloured globes were starships belonging to two different civilisations.