I'd put Copenhagen on par with London. It's cheaper than Stockholm and Oslo.
You wouldn't regret it. Copenhagen is a fucking sick city, and arguably one of the trendiest cities in the world right now. If you have even the slightest hipster inclinations you'll love it. Incredible food scene, fun nightlife, loads of culture and history.
It's the perfect city for a Friday-Monday get-away.
In the last two years I've had more friends contact me about things to see and do in Copenhagen than any time before. I've actually compiled a guide that I copy paste to them because it happens so often, and so far they've all really enjoyed the city.
Flights should be pretty cheap out of London too if you book in advance and the infrastructure in Copenhagen is second to none, so easy to get around and it's very walkable. The architecture in Copenhagen is pretty cool too because even though it's an old city we love combining modern architecture with the older stuff.
Let me know if you need any more info