For couples of mixed faiths, (where one of you is Church of England), or no faith it is possible to get married in church, but you will have to satisfy their requirements and understand that the ceremony will be the church of England service. That's non negotiable. If you are lucky you may find they will permit a reading or some music that reflects the other faith. Same sex and other faith couples may not have a church marriage.
Registrars will allow other faiths, mixed faiths, no faith or same sex couples to have a marriage ceremony, but it comes with limitations.
I welcome every couple; it's simple really, love is love and it comes in many packages. Every couple and every ceremony receive the same level of care and attention and every ceremony is written by me with love.