Currently in the UK if you are married, or in a civil partnership prior to transitioning, you must annul that marriage or partnership when you apply for your GRC. If you then wish to continually to be legally recognised as partners, you have to get married or make a civil partnership based on your new circumstances. It's not possible to get your marriage changed to a civil partnership, or vice versa.
If you are a British citizen or resident you can sign the petition being made currently to Downing Street at http://petitions.pm.gov.uk/certificates/ asking to allow a Gender Recognition Certificate to transfer a current Marriage License to a Civil Partnership License
(posted to transgender, polygenderuk, and own journal)