I did some more research after that post and found this explanation at [1]:
> Turing put this as follows: "an interpretive routine is one which enables the computer to be converted into a machine which uses a different instruction code from that originally designed for the computer".
It goes on to describe how Wheeler simulated a number of capabilities that EDSAC's hardware did not provide. Some more description of that is available at [2].
Finally, I found [3], which includes an actual listing of an interpretive routine for the EDSAC and a more detailed explanation. See page 47-48.
After seeing [3] it's like writing a bunch of EDSAC assembly then partway through, you want to work with floating point numbers, which no EDSAC instructions support, so you use a special code indicating your next several instructions are written for the "EDSAC+Float" machine instead, and they are interpreted that way.
This final document I located was quite interesting.
In the end, I think "interpretive subroutines" are perhaps closest to being like "virtual machines" or "emulators". Because there weren't really high level languages at the time, the concept in their mind is more like writing code for a different machine. It is like a high level language, in that it expands the set of operations that the programmer can use to speak with the computer.
[1]: https://books.google.com/books?id=uflV0_q-FEUC&lpg=PA190&ots...
[2]: https://books.google.com/books?id=AoWrCAAAQBAJ&lpg=PA33&ots=...
[3]: https://archive.org/details/programsforelect00wilk