Most British homes don't have air conditioning. As a nation we tend to be fresh air fiends - personally I sleep with a window open all year round and hate it when I travel in the US and find that windows are fixed closed in hotels because there's air conditioning.
If you want air conditioning you'll need a modern chain hotel (even then it's not absolutely guaranteed) or a modern hotel-style serviced apartment.
August can get hot - mid-20s Celsius is most common but low 30s isn't unheard of - and London can get stuffy. But it's so rarely truly hot in the UK for very long that we just don't "do" air conditioning in domestic settings.
Either fling the windows open or if it's important to you, find somewhere to stay that has it. Don't expect other nations to be exactly like the US in how we live.... you probably won't have a dryer in the flat, either (we tend to air-dry clothes).