"Placet is a Crazy Place" by Fredric Brown. If you read it about 50 years ago in England, it could have been in this anthology. Here is the summary from Wikipedia:
Placet is a fictional planet that appeared in the Science Fiction story Placet is a Crazy Place by Fredric Brown.
Placet is composed of both ordinary and heavy matter. The core is made of the collapsed, heavy matter, giving the planet a gravity three-fourths that of Earth. Bird-like animals made of heavy matter fly through the earth above the heavy matter core.
Placet revolves faster than the speed of sound in a figure eight pattern around two stars, Argyle I and Argyle II. Argyle I is normal matter and Argyle II is contraterrene or negative matter. Half way between them is a field where light slows to the speed of sound. This field allows Placet to be able to eclipse itself twice at the same time, run into itself every 40 hours and chase itself out of sight.
This field also affects the brains of human beings, resulting in extremely vivid visual hallucinations. The sense of touch is unaffected by the hallucinations.
And here is a passage from the story:
You can close your eyes, of course, but you don't--because even at the height of the effect, your eyesight gives you the relative size and distance of things and if you stay in familiar territory your memory and your reason tell you what they are.
So when the door opened and a two-headed monster walked in, I knew it was Reagan. Reagan isn't a two-headed monster, but I could recognize the sound of his walk.
I said, "Yes, Reagan?"
The two-headed monster said, "Chief, the machine shop is wobbling. We may have to break the rule not to do any work in mid-period."
"Birds?" I asked.
Both of his heads nodded. "The underground part of those walls must be like sieves from the birds flying through 'em, and we'd better pour concrete quick. Do you think those new alloy reinforcing bars the Ark'll bring will stop them?"