Pagan handfastings already have legal recognition in Scotland.
In 2007, a woman named Cassandra M set up a petition on the Prime Minister's petitions website to make handfasting legal (now closed). The response was that they had reviewed the Marriage Act previously but were unable to come up with anything sensible so it was dropped. Furthermore, they said,
Traditional Pagan ceremonies are held in the open air. All outdoor ceremonies in the UK need an additional legal ceremony for the marriage to be recognised by law.Well, Pagan ceremonies don't have to be held in the open air - even if we don't own many buildings, we can always hire them. Perhaps we need to re-open this issue with a slightly different wording of the petition.
I wonder if Hindu, Muslim and Sikh weddings are legally recognised under the current provisions for "Marriage solemnized in a registered building without the presence of a registrar, by the authorised person in whose presence the marriage is solemnized" which seems somewhat ambiguous - can Hindu, Muslim and Sikh celebrants be an "authorised person"? Why couldn't a Pagan become an "authorised person"?
Also, both Pagans and Unitarians would like the right to perform same-sex weddings.