A clear example with people-friendly explanation of how to fill in a marriage notification form is available on the website of City of Kobe. http://www.city.kobe.lg.jp/life/registration/koseki/img/konin_gaikokuj...
(1) You and she set a day for the marriage notification (during your stay in Japan) when both the U.K. Embassy Tokyo and a Japanese municipal office (e.g. Chiyoda City Office) are open.
(2) She prepares for the marriage notification: finding two Japanese witnesses (who each have reached the age 20), filling in her part of the notification form, etc.
(3) Each witness fills in the witness's part of the notification form and puts his/her seal.
(4) You get necessary papers ready for making an affidavit. https://www.gov.uk/marriage-abroad/y/japan/opposite_sex
(5) You come to Japan.
(6) You fill in your part of the marriage notification form.
(7) On the day for the marriage notification, you bring your necessary papers to the U.K. Embassy Tokyo, then make there an affidavit.
(8) You and she visit the municipal office; you bring there your affidavit and passport; she brings there her necessary papers (including the notification form), her personal seal and her (legally-authorized) ID certificate.
(9) She puts her seal on the marriage notification form, then submits the form with all the other necessary papers including your affidavit.
(10) After the marriage notification is accepted, she applies for a certificate of acceptance of marriage notification [ kon'in-todoke juri shoumei-sho
]; then she hands you this certificate.
Logically a marriage notification form can be submitted at any time; however, if she submits the notification form in late business hours or a closed day for the municipal office, it may take a few days to obtain a certificate of acceptance.
I recommend she takes two sheets of the notification form, one for a draft and the other for submission, leaves the date of notification unwritten until the day, and writes it when she actually submits the form.
Successfully accomplishing the procedure of marriage notification, you and she get necessary papers ready for your applying for a visa / the status of residence (for a spouse of a Japanese national).
Those papers may include her koseki touhon
which is newly issued after the marriage notification is accepted.