The apple pie

I'm no expert, but from the looks of that slice, it seems like she had a very tightly packed multi-layer of apple in there, and that possibly it had all cooled and congealed into a solid mass that kept it firmly together. That looked like a slice from a pie long-cooled, perhaps even from the fridge.

Apple pies in England are essentially not that different in recipe or result from American ones; I've not heard of a more cake-y one, no.

But I remember my mother's apple pies would -- if they lasted long enough to sit around in the fridge -- sort of congeal into something that looked as "firm" as that slice in the movie. His slice also looked massively thicker than anything I saw my mum make!

Do you mean a thick apple pie like the one in this recipe? I just give you the link but maybe it's not what you're looking for?
Best,
http://www.simplyrecipes.com/recipes/extra_thick_apple_pie/

I noticed that too myself about the Apple Pie being more firm than even my own would be after sitting in the fridge for a couple days. However, from what I noticed in this movie, even the Lemon meringue pie was HUGE. I wondered if it was just made to make the food actually become almost it's own character in the movie, larger than life as it were. I know I found my mouth watering at the food and that could have been what the filmmaker was going for. It could have just been to make the food really jump out at the audience.