I'm lost.
My understanding is that, when two people plan on getting married, each of them must 'give notice' at the registry office which is local to their usual place of residence. (It has absolutely nothing to do with house ownership. Someone could own dozens of properties all over the country but live at The Ritz in London. So it would be Westminster Registry office where they would be required to give notice).
The actual wedding venue is also unrelated to where notice has been given by either party. So a bride-to-be living in Suffolk would give notice at Ipswich Registry Office, while her future husband, who lives in Newcastle, would give notice in that city. They could then choose to get married in Ipswich, Newcastle, Birmingham, Exeter or anywhere else, as long as they do so within 12 months of giving notice.
As long as each of the people in your post give notice at the registry office that's local to them, property ownership and/or tenancy agreements simply don't come into it. So what are they worried about?