tall building for sightseeing in London

Possibly The Shard?
Edit to add a comparison as I was curious myself: here's a link for comparison of the two sites

http://golondon.about.com/od/planningyourtrip/ss/Londons-Best-Observation-Deck-The-Shard-vs-the-Sky-Garden.htm#step2

It was probably the Sky Garden at the top of the "walkie talkie" building.

https://skygarden.london/plan-your-visit

That has to be the Sky Garden, like the previous poster said.

Having done both of these, I will say that the two views are both good but different because they are located different places. On the Eye, you aren't as high up, and you're closer to Parliament, Big Ben, Westminster, etc., so you see those really well. The Walkie Talkie building is taller, and further east (and a little north). You see a more expansive vista, but the landmarks that are closer and thus more visible are Tower Bridge, the Shard, etc. So it's just a different view, but also great!

You can go up to the Sky Garden for free, but you have to get a ticket in advance, and they go almost immediately upon release, so pay close attention on the website to when that is. Once up there, they have a bar, so you can get cocktails, wine, beer, and depending on the time of day, snacks.

The Eye is purely a viewing experience. I've only done it once, but when I did it, the friend I went with insisted we look up the exact time of the sunset that day, and then book tickets that would put us on the Eye at that time. That turned out to be brilliant; it was so beautiful. So I always suggest that to people!

The Shard is very expensive.

You're already on the right track, but Rick's London book lists a dozen viewpoints, not all equally high, on page 90 in the current edition. Sometimes, it's from the top floor of a free museum, such as the Tate Modern or the National Portrait Gallery.

I also have my eye on someday trying the Duck & Waffle restaurant which is not only on the 40th floor of something (the Heron Tower) but also open 24 hours.

One New Change is a new retail/office building right behind St. Paul's. It has a glass elevator, too, and a restaurant on top. Unfortunately, it was raining the day we were there.

Thank you for posting this. I never knew about these options.

Thanks so much to everyone. I'm pretty sure it was the Sky Garden. As soon as I saw the name it rang a bell. However, I now also have a few other places to consider, like One New Change and also the Duck and Waffle Restaurant among others. I must say, I like the Duck and Waffle idea. I'll let you know if I get there. Again, thanks to everyone who came to my rescue.