For those old enough to have grown up before smartphones, the morning ritual would include asking about the weather before heading out to school or work. Maybe you looked out the window and guessed the rest of the day. Or, you turned on the radio for the daily report. If there were a morning newspaper delivery, the front page would have a small snippet with the 24-hour estimate.
While looking out the window was a lot more accurate for the current weather in your location, the forecast from a professional was still more assuring. Computers were much slower than today, so weather models were not great, but most days worked well enough so you could get on with what mattered.
The critical part of the process was what you did with the information. Did you choose to wear something specific based on what you were expecting? Was a jacket or umbrella packed for later use, just in case? What about what you wore on your feet? Did you adjust your mode of transport to avoid long walks in the rain? And where I lived, snow and ice were common, so there were even more adjustments.
The rule of thumb was this. Accept the imperfect prediction, create some options, and be prepared to get wet or change plans if you get it massively wrong. The perfect prediction was not crucial to success.
Given the climate in most of the UK, what is likely to happen in the next 24 hours is not all that varied once you accept you might get wet or remain dry. Having spent many years in London walking to meetings, an umbrella was enough most days to cover the risks. On days when I was not expecting rain and chose incorrectly, ducking under cover for a short period could be enough to get through the worst of it.