My understanding is the Commando kept the service number from their original regiment - who also paid for them.
In my granddad's case he had two serial numbers, an Royal Marine and later an Army serial number, which you can see documented in his service records.
http://www.commandoveterans.org/cdoForum/posts/list/3563.page
http://www.commandoveterans.org/cdoForum/posts/list/3577.page
I assume from this then that my father may have two service records?
As in my case, you should apply to the Royal Navy and Army records.