Thank you everyone for your help! I was in contact with London Wildlife Protection, who sent over a couple of lovely volunteers to pick up the pigeon. We?d checked on him 15 minutes before they arrived? but unfortunately the pigeon was nowhere to be found when they showed up. Hopefully he just needed a bit of rest and was able to fly away. I typically detest pigeons, but it?s sort of wonderful to see so many people care for their well-being. The kind folks at https://www.londonwildlifeprotection.org/ accept donations if anyone is feeling inspired to contribute to the cause.