Were you there recently? The reason I ask is because Friday, August 9th ( I think..it was a Friday), we were in the MK. My dd and I were waiting for wishes on Main Street by the train station and my dh and other 2 were upstairs at the train station.
This man came near us with his dd I think in a double stiller and with a HUGE cooler. It looked like it had wheels. I am talking 2 feet by 2 feet.
Of course there was a perfect spot for him to stand in front of us, we'll in front of the man I was next to in an
ECV. I told the man he needed to move and I was nice when I did. But then he chose to stand in front of my dd and me with his dd on his shoulders. Really? I was not nice and said loudly "oh great now we can't see." He got the hint and moved.
Anyway, back to the OP. I have taken a small lunch box into the parks. But it went in the stroller.