Oh dear I must chip in my two penny worth
The act is here - Civil Partnership Act 2004
http://www.legislation.gov.uk/ukpga/2004/33
and is designed to give civil partner the same rights as those who are married.
So the survivor of a civil partnership has the same rights as a widow/widower.
CIvil partners have to be of the same sex - see early sections of the Act - but can be hetero. I am not sure if many heteros would wish to civilly partner another man but there is no impediment
and finally marriage.
I am completely confused what legislation in London has to do with religious ceremonies - this betrays my catholic origins I suppose - I am aware Acts of parliament control the Book of common prayer but I know of no legislation controlling roman catholic ceremonies (currently in force that is). There is the Ecclesiastical titles Act 1868 passed when the roman dioceses were refounded by Rome - very carefully and with different boundaries and names - and the Act declared they had no force in Law. The ministry was afraid that sundry Bishops would turn up tothe House of Lords and demand seats.
Other than that,I dont see that any English legislation can vary the orders of the Bishop of Rome to his Popish and Roman adherents. As for getting the Muslims to carry out gay marriages I await that with interest.