There is only one marriage in 1910 -
Thomas M. Barlow married Constance Bull - W. Bromwich, volume 6b, page 1377
I think that perhaps the W. in Constance's reference on FindMyPast has come about by someone taking the W. (of West Bromwich) and attaching it to "Constance".

At this period in time only the first forename is entered in the GRO index, all other forenames are indicated by initials.
If you search, using FreeBMD, then you will find the entries, and you can view the original images for both entries, by using the "spectacles" icon next to their name.