IMO they nailed the whole 80s-vibe in this video.

http://www.youtube.com/watch?v=EUsbpmQ9-mc
Hmmmmm.....maybe it's:
a. The geometric shapes
b. Her "Flock of Seagulls" style haircut
c. The ping-pong synth
d. The pre-requisite dark tiled walls with white grout

e. The flourescent colors / lights
All the more interesting when you realize when the lead singer was born:

sortmusic.com wrote:La Roux are an English electropop and synthpop duo formed in 2008 in London, England, UK, made up of singer/synth player Elly Jackson (born Eleanor Jackson in 12 March 1988) and co-writer/co-producer Ben Langmaid.
Their music is largely influenced by 80s pop music including Eurythmics, Depeche Mode, The Human League, Heaven 17, Yazoo and Prince.