Green’s Dictionary of Slang

to eat, esp. heartily or greedily; usu. with a prep.; thus tuck in v.

1784		R. Bage Barham Downs I. 191: Let me be your physician [...] We will dine together; tuck up a bottle or two of claret .
1908		H. Green Maison De Shine 92: He’s been give sirloin steak [...] while the other boarders tuck round steak.