Searching for apps that will run on an original iPhone – excluding apps that will not run on iOS 3.1.3
Seeking an alternative to VintApps 3.1.3 led me to older Apps – MacRumors Forums (2013-11-05), there's a link to an Apple Club article: 

Finding iOS Apps Compatible with Older Devices

First impressions: useful, US-oriented. 

Adapted from what's there: I could use a Google UK search, such as the one below, as a basis for finding compatible apps in the UK App Store: 

https://www.google.co.uk/search?q=site%3Aitunes.apple.com%2Fgb%2F%20%22requires%20ios%202.0%7C2.1%7C2.2%7C3.0%7C3.1%22

… for example, a search for carshare-related apps.



Still, I'd prefer an app – ideally for OS X – with a smart user interface.