With a religious ceremony, it will, of course, focus on religion. God is mentioned throughout most of the ceremony and particularly in the vows. (I can send you a copy of the service, if you like?) Unless you go Unitarian, which is far more flexible.
If you do go Unitarian, you can have pretty much any sort of service that you like, assuming that the minister agrees that what you want is a good fit for you as a couple. My minister has done a lot of inter-faith weddings (Christian/Hindu/Buddhist/Muslim) and also one pagan wedding, and one wedding of two total non-believers! Their services are usually very similar to a CofE wedding, but they like to make each service individual to the couple.
We're not having God mentioned in our vows, and all the references to God will be open-ended and will specifically welcome non-Christian views (including atheist views) on what God is. It's important to us that our open-ended, spiritual views are represented in the service, and that people of all beliefs will feel included.
The down side is that there aren't many Unitarian chapels around, but the one we've chosen is gorgeous. No silly rules about being part of the parish, either, and he doesn't even enforce attendance before the wedding (which somehow makes us
want to go!)