Wow! Hope the lady was ok!
999 works from mobiles fine, I should know as I've had to call several times in the past couple of years - I seem to be the only person on the road who has good enough eyesight to see someone knocked off their bike, thrown from a horse etc, etc. Bit worrying to think of so many short sighted motorists on the road, as of course, no one could see someone seriously injured and not stop to help, could they?!!!
999 calls work even when there is little signal because mobile phone masts have to 'reserve' a certain amount of space for emergency calls - so even if the network is too busy to let you call other numbers, it is always worth trying. I've got through to 999 when my phone didn't appear to have any signal at all!