Quite right! I should have written "please help yourselves" (I am assuming that people are not served with the vegetables and have to help themselves!). An alternative phrase is "Bon appetit" or "Please start".Nor would I present someone with a plate of food and say, "Please help yourself", because that to me means "Please serve yourself", which does not fit the situation.
Try any episode of "Jamie's Quick & Easy Food". That's where I hear i"Tuck in" without excepion every episode. He is also a fan of "Whack it in the oven"."Dig in" is a common AE expression in the context of starting eating. I had never heard of the expression "tuck in" with respect to food until it appeared a few days ago in this forum (although I did know the Australian expression "tucker.")
I normally associate "tuck in" with putting infants to bed.