@Quincy
As I am sure you know, it can get chilly in the winter in London (and also the autumn and spring) so heating is really a must. Whilst most homes here have a gas central heating system with radiators in every room, air-conditioning is very rare in UK homes and hardly ever needed, but of course, with climate change, that might not be the case in the future! It's also useful to think about the varying seasons in terms of the bedding provided. I have lighter and heavier options for this and extra duvets and quilts available in the chillier months if needed. I even have hot water bottles and electric blankets for those guests who really feel the cold, although I would not say these are essential.
Decent WiFi is also essential. While there might be a few listings elsewhere in the UK that market a off-the-beaten-track, digital detox experience, I should think every guest coming to London would expect good WiFi. Conversely, my guests very rarely use the TV/cable package, so I'd say those were not really necessary as everyone seems to stream stuff on their devices here.
Breakfast is NOT an essential amenity. There are so many options nearby, whether that is cafes or supermarkets, and it's just easier for guests to buy what they like, when they like. I think I've only ever hosted one stay where the guests expected me to feed them. I think breakfast is rarely offered as an amenity in London.
There are a number of other amenities that I would consider essential, e.g. cooking and laundry facilities, but they are less to do with location and more to do with the fact that I host long term stays.