According to Wikipedia, as reported in Doctor Who Magazine Issue 418:
The eventual costume, in particular the bow-tie, was influenced by Patrick Troughton's Second Doctor, after Matt Smith fell in love with the Troughton story The Tomb of the Cybermen.
Smith's love of the Second Doctor was also reported on Digital Spy:
I love Patrick Troughton. [Troughton's 1967 serial] 'Tomb of the Cybermen' is one of my favorite stories. It's so creepy," he told Newsarama. "What I think is wonderful about Troughton is he's weird and peculiar but he never asks you to find him weird and peculiar. He was a great actor. And I think the Cybermen are as scary as they've ever been in that one story.
And looking around on SciFi and Doctor Who forums dated from that time, people made that connection right away:
When I read the description of the costume I thought a re-tread of 2nd Doctor.
and:
It's sort of a Patrick/David amalgam. I like it! (Looks more Patrick than David the more I look at it, not that that's a bad thing.)
There's also a somewhat detailed analysis from blogger comicgeekboy about the "homage" the Eleventh Doctor is to the Second aptly titled, "The Eleventh Doctor: A loving Homage of The Second Doctor".
I couldn't find any direct evidence that points to the Eleventh Doctor being inspired by Skinhead fashions, but given the Second Doctor was on the air around the same time the Skinhead culture was becoming popular, it's not inconceivable there's an indirect influence, there.