"proceed to dinner" is correct and usable in written English.
You can use this phrase when wanting to tell someone to go to eat dinner, for example: "Let's proceed to dinner. I'm hungry!".
No one was, and they then proceeded to dinner and the ballgame at the Brass Monkey sports restaurant.
Judging from their response, proceed to ask them out to dinner.
The evening started with cocktails, then proceeded to a dinner at the back of the restaurant, where guests sat at tables arranged in a square.
In a new Ariel commercial, the husband proceeds to cook dinner after a text from the wife about being stuck at work, and then, for the first time in the storied history of the Indian Husband in Advertising, washes his stained shirt himself.
9 45pm: Sit down at Makoto for dinner and proceed to order everything.
"It wasn't supposed to happen this way!" you sigh when your friend cancels dinner plans, and then proceed to hop into bed to read your favorite book for the eighth time.
"Riot" culminates in a set piece in which the lads hold a black tie dinner in an inn and proceed to trash it along with its owner.
