I live in Denmark, but when I travel to London I often stay at a Airbn and have found some really good places, especially one place I try to book everytime Im there. Its a good way to live homely, kinda cheap and also get some useful tips and etc.
But Read the reviews if you decide on Airbn before booking.
sometimes have good offers.
June is usually warm and a really nice time to be in Copenhagen, lots of exciting things happening.