"Will we all have to carry ID if we go to the supermarket?"
Probably not for supermarkets, or pharmacies, because the aim is to isolate for their own protection (they will be less likely to pose an infection risk to others) and people still need to eat and have medicine.
And it won't just be the over 70s, but also the medically vulnerable of all ages. So age based ID might not be the most useful measure. Countries who are policing movements do so by having people of all ages show why their journey/activity is necessary (aside from local food/pharmacy visits).
That'll be coming here soon. And I expect, as discussed on a different thread, checkpoints and cordons might be role for the military. Though of course existing security personnel couid already do this on private land