Composting in a small UK kitchen
Indoor systems solve the space problem. A bokashi bin is the easiest fit for a flat: it's sealed, so it doesn't smell if used properly, and it takes a wider range of food than an outdoor bin ever will. You add a bran inoculant, drain the liquid every few days, and after a few weeks bury the fermented contents or add them to a garden bin.
A wormery needs a bit more attention but produces excellent compost for pots and planters. Keep it out of direct sun, don't overload it with citrus or onions, and give it a home where you'll actually walk past it. Both systems are compact and work in a standard kitchen or under a sink, as long as you keep up with them.
Where it fits in a low waste home guide
Composting sits alongside the other zero waste kitchen swaps you'd make in the same room: plastic free food storage in jars and tins, a reusable produce bags guide for the weekly shop, and beeswax wraps usage and care for the bits that never get eaten.