where can I see the information on the CAA website specifically stating a UK EASA license does not need to go through the conversion?
An EASA licence does not exist and never has. Each state issues a licence of their own but in accordance with the EASA standards if it chooses. The UK has now withdrawn from the EU and the EASA agreements such that EASA no longer has oversight. Look carefully at the licence and it is obvious that it is not an 'EASA' licence but a licence issued in accordance with .......'
So if you have a UK licence then that does not require converting*. (The same is true for your UK passport by the way)
*The word 'convert' is much abused including by the CAA who should know better. It is very rare that a pilots licence requires converting; you can hold most licences independently from each other. You can hold both a EASA and a UK licence.