A Trace of Memory (1962) by Keith Laumer, probably. The text is available, legally and freely, at Project Gutenberg, here.
When Legion meets a strange old millionaire called "Foster,"" he doesn't know that his whole life will never be the same again. For "Foster" has a strange story to tell. Part of his story is contained in his diary, which not only describes things in the very recent past, but goes back for centuries. . .
Foster has hired Legion to help him regain his lost memory. Then both men are suddenly attacked by alien powers. They flee to Stonehenge in England where they discover a strange control chamber deep in the ruins.
They succeed in bringing down to earth an alien space ship which has been in orbit for thousands of years. Eventually they both become captives. . . on another planet.
More precisely, quotes courtesy of Project Gutenberg...
The older person (an alien) starts becoming younger...
The older person, in this case, being Foster.
It wouldn't do any good to turn myself in and tell them the whole story; they wouldn't believe me, and I wouldn't blame them. I didn't really believe it myself, and I'd lived through it. But then, maybe I was just imagining that Foster looked younger. After all, a good night's rest——
I looked at Foster, and almost groaned again. Twenty was stretching it; eighteen was more like it. I was willing to swear he'd never shaved in his life.
A cat is inside with him and he uses the cat's metal collar to dig himself out with...
Itz is the local cat.
Itz didn't seem to care. She marched around my head and back again, now and then laid a tentative paw on my nose or chin, and kept up a steady rumbling purr. The feeling of affection I had for that cat right then was close to being one of my life's grand passions. My hands roamed over her scrawny frame, fingered again the khaffite collar I had whiled away an hour in fashioning for her aboard the lifeboat—
My head hit the stone wall with a crack I didn't even notice. In ten seconds I had released the collar clasp, pulled the collar from Itzenca's neck, thumbed the stiff khaffite out into a blade about ten inches long, and was scraping at the mortar beyond my head at fever heat.
Found by searching this site for
[story-identification] stonehenge aliens which returned, among others, 60's 3-pt serial about a boy who finds an alien ship at stonehenge.