Is the change we're talking about limited solely to which countries remained part of the British empire or retained the British system of government? If so, you're absolutely correct.
If, however, we're using the word 'change' in the more usual sense of 'not remaining the same', then it's pretty far from correct. Every empire that's expanded - be it Greek, Roman, Spanish, British, or whoever else - has had varying effects on the areas it conquered. This includes, but isn't limited to, language, clothes, architecture, engineering, weaponry, agriculture and transport.
Are you suggesting that other than a civil service, you can travel to various countries that were once 'ruled' by Britain and see no remnants of it?