When I was doing mail delivery as a summer job, there always were experienced delivery pros available to help decode addresses (a win-win situation: the guys approaching retirement had less mail to deliver, so they had lighter bags, but they could only leave when all others were done sorting their mail). During the sorting job in the post office, you would find postcards in your lot that only mentioned the colloquial name of a bar, the colloquial name of a regular there and a city name. When you asked, they would immediately tell you "that's x street, number 45". They also often could give you a house number, given a surname and a street.

At first, that seemed surprising, but even after a few weeks, you start recognizing surnames and linking them to numbers. It helps that mail is not uniformly distributed over all addresses.

What I find more surprising about the UK is that thanks to the many post codes (and hence just a couple houses per post code), something like

  13
  AB1 CD2

is an absolutely unique address.

Yes. Here a lot of websites just ask for house number and post code and then look up the full address in the PostCode Address File.

The trade-off, of course, is that one needs to know the exact postcode of an address. Back in Germany, most (small) towns only have exactly one postcode (5 numbers), and even in larger towns, one postcode often covers about 10000-20000 people, so it is relatively easy to remember the postcode for a large geographical area.

But I guess this doesn’t matter all that much since you can look up addresses online nowadays and remembering numbers seems to be as antique as the job done by the people in the OP.

There is no trade-off: In the UK, postcodes are much more specific, and there's always manual address entry.

Unless ‘manual address entry’ implies that the postcode is not a necessary part of an address, then there is the trade-off that postcodes in the UK are (basically) recipient-specific, whereas postcodes in Germany are town-specific. If I know my parents’ postcode, I know the postcode of someone living three streets away from them and hence only have to remember the street name and house number, whereas I need to remember the postcode of that particular recipient to address a letter in the UK.

However, as I said, such data being easily available nowadays renders this point somewhat moot.

I don't understand. Why are you mentioning the trade-offs of doing this in Germany when I'm talking about the UK?

Even so, postcodes in the UK aren't town-specific, they're more like street-specific, roughly.

I am comparing very specific postcodes (as in the UK) to very broad postcodes (as in Germany). While the former allow for very simple addresses (street number + post code), they come with the trade-off I mentioned.