Here are the climate-related sections of speeches by MPs during the Commons debate Marriage (Same Sex Couples) Bill.
Full text: https://hansard.parliament.uk/Commons/2013-05-21/debates/13052156000001/MarriageSameSexCouplesBill
18:50 Diane Abbott (Labour)
Some people listening to this debate will be thinking, “This is all very well, but there is war in Syria, climate change and a huge economic crisis, so why does this matter?” Let me tell the House why it matters. When this legislation finally goes through, there will be adolescents going to bed that night who are struggling with their sexuality and who, knowing that the law has gone through, will think as they go to sleep, “Maybe it’s not so bad. Maybe my life isn’t ruined. Maybe I can find some acceptance. Maybe I can come out to my friends, and maybe even to my mother and father.” If this debate and this legislation makes the lives of so many hundreds of thousands of young people just a little better, we will have done great work in the House tonight.
[Source]