Behind St. Pauls, about a half a city block, is a shopping center/business park called "One New Change". Go in, and take the elevator to the roof terrace. Unbelievable views of St. Pauls, and the river and "The City". I spent an hour there last May as a thunderstorm was moving in. Wonderful memory. No crowds.
Nice bit of info. My London Secret is the hidden park next to St. James of Piccadilly church. There's a Caffe Nero so you can enjoy your cuppa in the park for a nice respite. I enjoyed watching shoppers on the adjacent Jermyn Street. The only downside is a gawdawful metallic sculpture. NOT a thing of beauty. What were they thinking when it was placed there?!?
Maybe not so much of a secret, but it's kind of out of the way from central London: Crystal Palace Park. Back in Victorian days when they started discovering dinosaur fossils and putting them together, they made lifesize models of them to show to the public, and they can now be seen in that park around a small lake with an island in the middle. The thing about them is, is that don't really represent dinosaurs as we know them today (with 150 more years of discoveries and research). It's quite interesting to see these dinosaur statues as the Victorians perceived them to be, with the knowledge that they had at the time. They're shown in "lifelike" poses, rearing out of the lake or on the island. If my memories serve right, there's even a "fight" between two of them.
Also in Crystal Palace Park are the ruins of the original Crystal Palace that burnt down, but the stone foundations are there. It makes for a pleasant stroll.
The views from there are memorable.
Last year there was construction on the north side of St. Paul's (not the cathedral itself), but maybe that is completed by now.