I saw this on Gary's Flickr, and lodged it on my list. I was investigating some tunnels nearby, and it seemed rude not to pop up for a look.
Adelaide House was built in the Art Deco style in 1925, and reaches 43m high. It was one of the first buildings in London to have air conditioning, an internal mail system and once upon a time it's own rooftop putting green. It's commonly said to be the first modern office building in the City of London.

Taking in a quick prayer before hand, it was on with the ascent. very late in the evening, there was still a woman working away. Others have also come across this problem. Waiting for the right moment, I continued on up, keeping my eyes open for security or other office workers looking out of the numerous windows.
At the top, I climbed onto the roof of the air conditioning and lift assembly to get the highest possible views. Looking North to the City skyscrapers.

Looking West down the Thames

And South to the Southern end of London Bridge, with Southwark Cathedral and the Strata Tower.

East up the Thames and Tower Bridge

And over the roof, St.Magnus-the-Martyr's church, and the City again in the background. The fire escape stairs on the bottom left are part of Adelaide House, as it forms a right angle. It's not a rectangular-like building as the establishing shot at the top suggests.

I then dropped down to the actual building roof, presumably the putting green would have been here at one time. Now just the remains of a failed skydiver.

A wide shot of the Southern Bank of the Thames and London Bridge. The bright lights of the Shard going up.

A final attempt to capture Tower Bridge, and then time to pack up and leave.

A pretty straightforward explore, all things considered. Apologies for lack of tales of daring do, fighting off squads of elite security ninjas and minefields.