Though he did endorse gay marriage in the House of Lords, he said the following in support of same-sex relationships.
It is clearly essential that stable and faithful same-sex relationships should, where those involved want it, be recognised and supported with as much dignity and the same legal effect as marriage. Although the majority of Bishops who voted during the whole passage of the Civil Partnership Act through your Lordships’ House were in favour of civil partnerships a few years ago, it is also absolutely true that the church has often not served the LGBT communities in the way it should. I express my sadness and sorrow for that considerable failure. There have been notable exceptions, such as my predecessor, the late Archbishop Ramsey, who vigorously supported decriminalisation in the 1960s. It is also necessary to express, as has been done already, total rejection of homophobic language, which is wrong and, more than that, sickening.
Entire Debate found here. The Archbishop’s comments can be found at 3 Jun 2013 : Column 953