Lyric discussion by RommelDAK 

Cover art for No Action lyrics by Elvis Costello

Ahhhh, a bakelite is an old fashioned phone--now I get it!

http://antiquephones.blogspot.com/

Bakelite was a phone, so there's that, but it was called that because the body of the phone was made from Bakelite, one of the first commercial plastics. So he's also saying that when he holds her, she's as dull and lifeless as plastic.