I used to live in a shitty old Victorian conversion flat, the kitchen could only fit a small undercounter fridge with a tiny freezer box. I had to buy a tabletop freezer and make do with the small amount of fridge space, it was quite fortunate I only lived a couple minutes from Tesco so could shop for a small amount every day. I was living by myself, no clue how you would handle it if you were living with someone else.
In most places nowadays you would have a full-sized fridge-freezer which is usually enough space, but if it isn't you might have a chest freezer or something in the utility room or garage. These are quite a bit smaller compared to a North American fridge, you can buy what we call American-style fridge freezers but they're quite expensive.