Before eating, we sometimes say "Let's eat!" or sometimes we also say "Dig in!" However, you would only say them in informal situations.

For　行ってきます、you can just say "I'm leaving" or "goodbye"

Hope this helped!

I've noticed that too, with Japanese, and I don't really think there's a direct translation, since いただきます and 行ってきます are sayings that apply to Japanese culture. Like... we might say general things before eating, or leaving the house, but they can vary greatly..... we don't have a set phrase to say on these occasions, ritualistically, I guess.

いただきます: Like Alex said, we could just say "dig in" in informal situations. In a family situation, depending on how religious one is, some families might "say grace" by saying a prayer, or what they're thankful for, but it varies from family to family. In a formal situation, I suppose it could get kind of awkward, wondering when you're supposed to start eating because there isn't a real いただきます we commonly say.

行ってきます: When we leave the house (or office, school, etc.), we usually say things like: "Bye mom, love you." or "See you later." "see you tomorrow" or just... "Bye." Depending on one's family, it might be rude to leave without saying anything similar to 行ってきます, or "I'm leaving", but saying that isn't expected as it is in Japanese.

So overall.... I agree there isn't really a direct translation, because culturally we don't have formal expressions like いただきます or 行ってきます to transition from not eating to eating, or leaving home/work/school.

I once saw a Japanese drama with English subtitles that translated いただきます into 'Grace'. Like what Alex and Hana commented, 'Let's eat!' or 'Dig in!' might be similar expressions in informal contexts. In my country, as a result of the influence of Japanese media, some people say 'Itadakimas!' before their meals. ^_^

As for 行ってきます, I would agree that 'I'm leaving' or 'Goodbye' are similar expressions. In an informal context, 'I'm off!' might be close in meaning too. (I've seen some of these expressions used in anime or drama with English subtitles.)

Thank you so much Rose!
I wanted to know them. (^^ゞ

Well, I am not a proper person to answer your question.
so, I decide not to say anything. haha... just kidding!!

I agree with the above comments. However to add something to it, people sometimes say bon appetit! Which literally mean good appetite, or could be used like "enjoy your meal".

Hello Alex, ^___^
Thank you so much for the nice explanation.

Hello Hana, ^__^
I like your name. I guess it means "flowers" and thank you so much for the nice explanation. ^^

Hello Darkhonhour, ^__^
Thank you so much for the corrections and a nice explanation.

Hello keikoさん＾＿＾
You are very welcome.
Please vist my page again.^^

Hello shifu, ^___^
Haha... no problem.
You are always so funny.
Thank you so much for your frequent visit to my page. ^^

Hello ジャス　＾＿＾
Thank you so much for teaching me another nice expressions.
It sounds like French. ^^