Blur are my second favourite 90's artist after Radiohead so I wouldn't argue with people putting him up there. Thom Yorke will always be number one but he is in the list of many different songwriters that could be number 2.
Although saying that I always felt that Blur are a great band predominantly due to Graham Coxon. Damon Albarn is certainly a good songwriter but he is not in the same level as Ray Davies or other great 60's songwriter. Blur would have been a derivative nostalgic act if it wasn't for Graham Coxon guitar playing which gave it a unique aspect. He is great at countermelodies and he also introduced 90's alternative influences that makes Blur's a 90's group rather than a retro group.
Although lot of people disagree (considering that there are plenty of Gorillaz fan and they have the same or even greater status as Blur) but I don't think Damon Albarn hasn't really achieved much post Blur (I know people consider him gravitating towards hip-hop as a positive and puts him in the sort of Peter Gabriel category of moving from a culturally white genre Britpop/Prog Rock to culturally black genre of hip hop/world beat but IMO Gorillaz weakness is that he dabbles in hip hop) while Graham Coxon solo career is pretty great.
If we exclude earlier 60's 70's 80's songwriter who were still writing great music (you could argue that Paul McCartney and Ron Mael was the greatest songwriter of the past 30 years but that's not within the spirit of that question I believe).
Other contenders outside Thom Yorke and Damon Albarn
Flaming Lips (since all the songs are credit to the band, I have no idea who writes all the song)