There is no single conversion between RGB and CMYK and certainly RGB<=>CMYK is not an identify function.
Which CMYK? There are any number of different CMYK color spaces.
Which RGB? sRGB, AdobeRGB, something else?
Microsoft Office is totally an RGB application that implicitly is sRGB. You cannot enter RGB values for text or graphics and expect that the resultant PDF file is going to render those RGB values with any particular CMYK value.
The “fix” is not to use Microsoft Word for color-critical applications that depend on specific CMYK values!
Quote: "Looked for the RGB values of the CMYK house style colour in Illustrator and Photoshop."
Not the most accurate way to generate values between CMYK and RGB. Depends upon which color space / color management was used in Photoshop or Illustrator. You'll get different CMYK build numbers from the same RGB color.
Plus, they're Adobe's subjective conversions. Everyone's -- or every tool's -- will vary.
When the document is printed, no RGB color will appear "correct" in CMYK. This is a law of color science: RGB is additive color, usually viewed on a backlit screen, and contains millions of colors. CMYK is subtractive color, printed with tangible inks/toner on tangible paper, and can replicate only thousands of colors.
The 2 will never be the same.
So choose the best CMYK color build that approximates what you see in RGB, and be done with it.