I started off like you. At first I thought that my wife and I only needed a CENOMAR, but that turned out not to be the case. And although a Philippine CENOMAR and a UK CNI are similar if not the same, it is not enough to aquire a Philippine CENOMAR on its own, hence we have to go through the ballache of getting a CNI too. Not only that, when you get your CNI you have to exchange it for a local CNI in the Philippines.
Hope that helps.
CENOMAR and CNI are pretty much the same thing. One is a certificate of no previous marriage, the other is a certificate of no impediment to marry. ( I think).