If Prifddinas Cymru ydy Caerdydd" translates to Cardiff is the capital city of Wales, and Llundain ydy prifddinas Lloegr means London is Englands capital city/ or Englands capital city is london. What specifically is the reason why one is the other way round as surely all three translations mean the same thing. so Caerdydd ydy prifddinas Cymru is Cardiff is Wale's capital city.
Cardiff is the capital city of Wales is the same as saying Cardiff is Wale's capital city for example.
Yet saying London is the Capital city of England is wrong.