Is shipping food legal?

The movers are coming tomorrow morning and I realized that I have the equivalent of two medium sized boxes of food. All of the items are sealed--dry, canned or spices, so they don't pose a huge rodent risk. But I realized that I don't actually know if the movers are going to be willing to pack it for me, or if I should try and pack it up and see if they will just let it go.

I know that I can't bring plants, so I'm not sure. But I don't know if that's the rules of the movers or customs.

Any suggestions (quickly!) would be very much appreciated.

(ps. I'm going to Republic of Ireland, but the UK, but I figure that the rules are probably very similar. Going to the UK next--already have a work permit!)

I would suggest you leave the food there.  Our shippers gave us the same info about not bringing food in our shipment.  I recommend you not bring it since it can cause a delay in your shipment.  Also there is a fee of around $500 if the dogs smell something or the customs officials suspect anything and they have to open your shipment for further inspection and then the stuff will also probably be confiscated.
As for spices and special foods you want to bring with you, I suggest you bring them in your suitcase.  If that's too full, then pay for an excess piece of luggage (rubbermaid container) and fill it with the desired items up to the amount of weight that your airline allows for baggage.  good luck....

The only info I could find was this:

http://www.fsai.ie/service_contracts/Customs/mou_ce.pdf

Article 5 says:

It is acknowledged that Customs may not seize or detain any non-animal food
products being imported from third countries unless the products in question are
prohibited to be imported by Irish national law (viz. by an Act or a Statutory
Instrument) or by EU Law.

I think that means I can bring stuff in? I'm having a hard time understanding this.

I'm not sure on the detailed rules, but there's no blanket ban on the importation of all foods.   

A few years ago I used to get cakes sent over from this place for Christmas.

We brought over quite a bit of food, and we paid a fair chunk to Customs for it.  (Homemade stuff, mostly... pickles, spices..).  So, no problem, but it would have been free if we could have fit it in our suitcases.

Meat and fish products are not supposed to be brought here... but we cat food with us, and again, no problem.  (I showed it to the agent at customs.)

I think that as long as it's nothing that needs refrigeration or is agricultural it should be ok. I know I was looking at that for mailing things, so I'm assuming it's the same for shipping things when moving.