No, the theme for Trigger Happy TV is not "Connection" by Elastica. It is, however, a blatant, shameless rip off of "Connection" by Elastica. I'm frankly stunned Elastica hasn't sued. T'would be particularly ironic and "postmodern" since Elastica were themselves sued for ripping off the opening riff of "Connection" from a song by Wire called "Three Girl Rhumba" off of Wire's album Pink Flag.
I think you might be wrong about it not being Elastica singing the theme tune Connection as it is on the Trigger Happy CD that I have and I dont think it would be on there if not the version used?