I went (for work, long story) a few years ago and while it's expensive, it's not scary expensive like Norway or Switzerland.
There's some prices here:
www.lalandia.dk/en/billund/eat
Obviously you'll have to convert to £s but I think those prices are around £20-25 for a meal, unless the exchange rate has shifted massively.
I never think of '£ per day' because I just try to get the best value, eg one meal out a day, take food if you can, make your own sandwiches, buy drinks, snacks, basics like eggs in the supermarket, that sort of thing and pay for everything using a card that doesn't charge for exchange. I do remember that they charged extra for credit cards, so in case they still do, despite it being illegal under EU law, make sure you have a good debit card (look on MSE if you need help with this) and put a load of money on there.
Remember that there's 3 people going who are quite capable of preparing food and something like supermarket pizza is a good way of having dinner that most people enjoy, on a budget without having to make any effort to cook.
Or look into Smorgasboard and make those.