"Crikey, that sounds either incredibly disorganised or incredibly thoughtless of Dulwich if they’ve only posted out interview letters today!
"What if your interview is Monday? - it doesn’t give you much time to organise time off work if you don’t get the letter until the weekend confused"
It's not quite like that. It's not a wrong description, but it's not complete, so it's misleading.
They ring those they want to interview: as I posted above: "For DC, good news is a phone call (and they sometimes ring well into the evening) offering an interview time. Letter/email confirming it follows (if they still bother with those)"
It seems they do still send a confirmatory letter. And they they are posted the same day as the 'no thanks' letters.
But yes, they do expect you to be available for the interview slot. The days they interview are published well in advance, and although stuff does come up, there is an expectation that you will plan for your child to be able to attend.
All SW London schools are rather like this - they are fitting in a lot of interviews in a short time, and need it concluded by a (loosely) co-ordinated offers timetable. They need their interviewees to be available in interview days. DC publishes its admissions timetable a year or more in advance, so there is plenty of notice of key dates.