I feel like the answer is obvious but I'm going to ask anyway: if I were to take the programs from one of these books and code it into this machine, is it likely to work?
Anyhow, you're question. Unfortunately no. You'll find that some parts of the program will work fine but Microsoft BASIC (which is what the Commodores ran and what this seems loosely based on) weren't entirely compatible with BBC BASIC.
BASIC in the 80s was a bit like Javascript in the 00s in that every browser did things did things subtly differently.
As an aside, I was playing on my BBC Micro last night. :)
That leads to the obvious question whether there are there more modernized BASICs out there now. Is there a standardized ES6 equivalent, perhaps? ;)
MS Basic kiiinda became as close to a defacto standard as can be described, just because it was the most common and commonly imitated.
In terms of a modern standard, there's quite a few modern BASICs, but the same kind of applies: Microsoft kinda leads the field. Many of the surviving projects are either directly or indirectly based off of QuickBasic and Visual Basic, or at least heavily inspired by them.
In terms of experience though it's nothing like the basic on these machines. Shell scripting with curses is probably the closest modern equivalent.
* FreeBASIC
* QBasic64 (an unofficial continuation of MS QBasic)
There is of course also VBScript / VBA and VB.NET but I think it's a bit a stretch to put them in the same bracket (particularly with VB.NET). It is a little like calling C# a dialect of C.
As mentioned by someone else, QBasic is still around, and there's also Gambas (which is as close to old-school VB as one can get on Linux) if you're looking to play with something.
https://en.wikipedia.org/wiki/Input_(magazine)
They did not do things subtly differently, rather completely different, depending on the model.
Few have managed to make me feel as old with as few words.
While as others have pointed out the specific BASIC programs are likely to diverge in various ways. That said, they're likely to have enough similarities that there are decent chances you can type in quite a few things and mentally translate "as you go".