I live in Brighon Pavilion, although might not be by the time of the GE.
Firstly, there are generally favourable demographics - however, I don't have time to give examples without resorting to listing stereotypes (eg the prevalence of hippies, hipsters, students, certain types of professionals) which would be a misrepresentation of both Green voters and the city as whole even though some of such labels might be accurate when applied to myself. The demographics shifted over the last few decades due to migration from other parts of the UK (London in particular) and from former students of the two universities remaining in the city.
Secondly, the Green Party have had a presence on the local council since 1996, which has expanded to the point whereby, as of 2011, they are now are the largest party and head a not un-controversial minority administration.
Thirdly, the Green Party (as opposed to the Lib Dems) were locally the key beneficiaries disaffection with the 1997-2010 Labour Government over issues such as the UK's involvement in the 2003 invasion of Iraq.
Finally, with regards to 2010, the Green Party heavily targetted their resources on this constituency because it was their best change of a win by about a million miles. The high public profile of the candidate, then-leader Caroline Lucas (who I'm acquianted with and rather a fan of), was definitely a factor in attacting activists from other parts of the UK and in attracting voters locally. In my opinion any other candidate would probably not have won.
