The practical thing to do right now is find out which water company actually serves your address, then check their website directly for what's currently in place - don't rely on national news summaries because the rules vary wildly by region. I've got family in a couple of different areas, and one's been under restrictions for months while the other's barely affected, so it really does matter where you physically are.
From what I've seen happen with my relatives, the progression goes like this: first come the appeals to use less water voluntarily, then hosepipe bans kick in (meaning no garden watering, car washing, that sort of thing), and if it gets worse they move to meter-based charges or actual usage limits. The people already living under restrictions aren't facing catastrophe but they do have to change habits - it's more annoying than frightening. Showers become quicker, you stop watering the garden, you stop refilling pools. Life continues, just with less waste.
That said, whether you personally need to worry depends on the specifics of your area and whether rainfall improves over autumn and winter. The six regions declared severe are obviously the ones where things are tightest, but even those aren't at the stage where taps are running dry. It's more that authorities are acting early to prevent that from happening. If you're outside those zones, keep an eye on your supplier's updates but don't panic - but if you're in one of them, start adjusting water use now rather than waiting for a formal ban notice.