Single track country roads are common, but rarely required except for the last little bit of the journey. Unfortunately some route planners seen to like to shave a couple of minutes of the trip time by using miles of them. I've come across a good few in France too. Widening would be very expensive (land purchase as well as construction) and being so old they tend to be too bendy to be fast anyway.
In urban areas, the roads and the houses they serve aren't so much narrow as used to store too many cars - when much of our housing stock was built, car ownership for normal people wasn't a thing.
The network of main roads should get you very close to your destination, so you only have to use such narrow roads for the last few miles (with exceptions for some very rural areas, but they're still not needed as through routes). Motorways (blue signs, numbered Mx or Ax(M)) are high capacity, with wide lanes and are intended to be the first choice for long distance (e.g. the M4 from London takes you to near Bath). There are dual carriageway A roads (overlapping eith designated "trunk" roads) to a slightly lower standard. Then you have single carriageway A roads, like the A46 that links Bath with the M4. Another quick road despite the cotswold hills. These can also be classed as trunk roads. Most villages can be reached by B roads which are often wide enough for a lane in each direction, but not always.
Given all that, country lanes don't need to be fast roads. In fact in some places where a road is just wide enough for a central white line, it's omitted to encourage slower, more cautious driving.
As for parking spaces, it's largely a matter of old standards being based on the typical cars of decades ago, which were far smaller than much of what you see now. There's little incentive to repaint bigger spaces to modern standards as you can get more cars into smaller spaces - more profit if you're charging for parking. Even if parking is free as at a supermarket, repainting costs money and reduces capacity for customers. I drive a Transit campervan, and for width it's OK in a typical supermarket space (being careful as I open the door). That struggles with length, but the solution is normally to park at the furthest edge of the car park, where I can overhang the back of the space, and if I o stick out, I'm not massively in people's way. That also generally means I can have a free space on at least one side.