The couple can't non-registered their marriage. It is not in their power to do so. When (and if) they married they had a registrar present, either at the registrar's office or at a non-conformist church. In the case of the Anglican church the vicar would act in the place of the registrar. These officials were responsible for seeing that copies of the certificate of marriage went to the local registrar's office, where the local registrar was also responsible for making sure a further copy was made of each certificate and sent onto the General Registry Office in London (hence when you purchase a marriage certificate from them you are always seeing a copy of a copy, not a copy of the original certificate). The officials present at the ceremony therefore register the marriage not the couple.
Reasons for why you might not have found the marriage you are looking for.
There may have been some impediment to the couple marrying e.g. a previous marriage, or the marriage if it occurred, would have been within the prohibited degrees (e.g. sister of dead wife or brother of dead husband) so they in fact did not marry, or married far later than you would expect and out of area.
They did get around to marrying , just not when you expected it. I have found marriages several to many years later for no reason I can see, the couple chose not to marry until later.
They did marry but one of them at least married in a surname you were not expecting e.g. the women was a widow, something you have not picked up from the birth certificates of her children which only give her maiden name.
One or other or both of the couple are missing from the GRO index because of the faulty nature of the index itself (something I have already touched on). If they married out of area your trawl of the local registrars' offices or the incomplete BMD (for I think only parts of Staffordshire?? and not the surrounding counties) would not find them. If you have only checked FreeBMD for the GRO index then you might not find them because this transcription is also incomplete.
Or finally they just didn't get married - something a surprising number of couples chose to do in the C19th. After all unless they were middle class with property and money to leave, marriage was not a financial necessity. The church demanded a ceremony should occur, but up until Hardwick's marriage Act of 1753 clandestined marriages were acceptable as was the old tradition of jumping back and forth over a broomstick.
What was the name of your couple and where were they in 1881?
Regards
Valda
