We are landing in London at 12:00 pm on Sunday March 21, and was wondering if my family and I have enough time to see a little bit of London. Not too much, just a nibble. Thanks! Our plane leaves for Rome at 19:30
Sure, you can nibble. But obviously you want to head back to the airport with more than enough time to make your flight.
Pick the one site you most want to see, or better yet, the one area/neighborhood and focus on that. For example, you could simply wander around Westminster and see Parliament (incl. the Big Ben tower), Westminster Abbey, Trafalgar Sq, and Buckingham Palace. You wouldnt have time to go into any of these sites, but you could admire the architecture and soak in the atmosphere. Find a place to sit and people-watch.
I had a similar 6 hr layover on a bus trip one July, and spent the time just walking London. In that time I was able to see Parliament, Big Ben, Trafalgar Square, Admiralty Arch, Buckingham Palace, Westminster Abbey, Piccadilly Circus, and a few other sites.
Didn't really take the time to go into any thing, but it is still to date one of the most fun days I've had in all of Europe.
PS - All done by walking. I'm a big guy, so I wasn't moving fast, and it was quite doable.