Clarified this is C++ source and not header-only. Added Android build options and excluded BC7 mode 6.
Single File Basis Universal Transcoder
The script combine.sh creates an amalgamated C++ source file that can be used with or without basisu_transcoder.h. This isn't a header-only file but it does offer a similar level of simplicity when integrating into a project.
Create basisutranslib.cpp from the transcoder source using:
cd basis_universal/contrib/single_file_transcoder
./combine.sh -r ../../transcoder -o basisutranslib.cpp basisutranslib-in.cpp
Then add the resulting file to your project (see the example files).
create_translib.sh will run the above script, creating the file basisutranslib.cpp.
Why?
Because all it now takes to support Basis Universal is the addition of a single file, two if using the header, with no configuration or further build steps (the out-of-the-box defaults tailor the included formats for various platforms).
The library is small, adding, for example, 249kB to an Emscripten compiled WebAssembly project (with transcoding disabled for BC7 and ATC; disabling ASTC can remove a further 64kB, and gzip will approximately half the wasm file).