4 punctures in one week, even after replacing tube and tire, what's happening?
The answer to my question -- why did my bike puncture four times, even after replacing the tube and tire -- turned out to be: bad luck. 

The first three punctures were caused by some damage in the tire (the punctures on the tube were all on the tire side). After I replaced the tire, I got another puncture - but this time the puncture was on the part of the tube facing the rim. On inspection I was that my rim tape was protruding up at the point of the puncture. Because I had a new tire and tube I had pumped the wheel up more than usual, which perhaps meant that rim tape protrusion was now a problem.

So, four punctures in one week: three from the tire, one from the rim.

For anyone else experiencing a confusing series of punctures, consider that you may be unlucky and that there are multiple problems in your wheel!