Just to update this, the standard now is:
<input type="file" name="image" accept="image/*" capture="environment">
to access the environment-facing (rear) camera, and
<input type="file" name="image" accept="image/*" capture="user">
for user-facing (front) camera. To access video, substitute "video" for "image" in name.
Tested on iPhone 5c, running iOS 10.3.3, firmware 760, works fine.