Immediately before 1837 the only legal places to marry were the Church of England and the places of worship of Jews and Quakers, but the legislation that introduced civil registration in 1837 also made it a possibility in other non-conformist churches, and brought in civil ceremonies in a register office.
To begin with not many non-conformist churches had their own registers, so the registrar had to attend; on sites like YorkshireBMD (the one I'm most familiar with) these marriages are listed as taking place in a "Registered Building (registrar attended)", or words to that effect. This means that access to the registers is more or less the same as if it had been a civil ceremony.
