diff --git a/ChangeLog.d/makefile-python-windows.txt b/ChangeLog.d/makefile-python-windows.txt
new file mode 100644
index 0000000..57ccc1a
--- /dev/null
+++ b/ChangeLog.d/makefile-python-windows.txt
@@ -0,0 +1,4 @@
+Bugfix
+   * The GNU makefiles invoke python3 in preference to python except on Windows.
+     The check was accidentally not performed when cross-compiling for Windows
+     on Linux. Fix this. Fixes #4774.
diff --git a/programs/Makefile b/programs/Makefile
index 997c198..55ebd60 100644
--- a/programs/Makefile
+++ b/programs/Makefile
@@ -43,11 +43,15 @@
 ifdef SHARED
 SHARED_SUFFIX=.$(DLEXT)
 endif
-PYTHON ?= python
 else
 DLEXT ?= so
 EXEXT=
 SHARED_SUFFIX=
+endif
+
+ifdef WINDOWS
+PYTHON ?= python
+else
 PYTHON ?= $(shell if type python3 >/dev/null 2>/dev/null; then echo python3; else echo python; fi)
 endif
 
diff --git a/tests/Makefile b/tests/Makefile
index 6695437..251a9c6 100644
--- a/tests/Makefile
+++ b/tests/Makefile
@@ -50,11 +50,15 @@
 ifdef SHARED
 SHARED_SUFFIX=.$(DLEXT)
 endif
-PYTHON ?= python
 else
 DLEXT ?= so
 EXEXT=
 SHARED_SUFFIX=
+endif
+
+ifdef WINDOWS
+PYTHON ?= python
+else
 PYTHON ?= $(shell if type python3 >/dev/null 2>/dev/null; then echo python3; else echo python; fi)
 endif