When D1 applied for 2020 entry, the email inviting her for interview arrived on the evening of 29th November, she had to be in Oxford from 10th - 14th Dec, so 11 days notice.
Oxford has an interview timetable www.ox.ac.uk/admissions/undergraduate/applying-to-oxford/guide/interviews/interview-timetable2
They say that you may only be given a week's notice of being shortlisted.
As others have said, O and C have very different approaches to interviews - Cambridge interview about 85% of applicants, while Oxford aim to interview about 3 people for every place, which is less than half the applicants.
D1 is now in her 3rd year of a History Joint degree at Oxford. Fwiw, she found the HAT interesting but tricky, had no idea how she had done. She could not submit the written work she had wanted to (long and horrifying story, haha), thought one interview had gone quite well and she really enjoyed it, wasn't sure about the other one. (She had one interview for each subject and then had to stay in Oxford for a few days in case she was sent to another college to interview - she wasn't).