No mention of beetle-crushers or drainpipe trousers in the lyrics?
And they generally call their waistcoats "drapes" short for drapecoat which isn't cut in at the waist--a boxcoat, I guess. The pockets, usually 3 or 4, are always lined with velvet as are the cuffs and collar. The drape's lining is often done up like the Confederate rebel flag of the American civil war but the Brits don't associate it with the Southern cause since they're workingclass Brits who could give a shit. They wear it because it symbolizes rebellion and rocknroll.
A tie is worn but are often string ties of the type worn in the American west. Sometimes a cowboy-type stetson is worn with it. The hat is optional because most Teds are proud of their quiffs--their greased hair piled high and combed back--and like to show them off.
Teddy comes from King Edward VII who was affectionately called Teddy by the British media. The fashion worn by Teddy Boys was popular in Edward's day (he was Elizabeth I's son and reigned from 1901-1910). So it is aften called Edwardian fashion. It was actually made popular by gay men during in WW2 where it functioned very much like the zoot suits did in America. In fact, the Teddy clothes ARE zoot suits.
The Beatles were Teddys but wore leather. Many Teds actually wear leather and are indistinguishable from greasers. Some Teds wear the Edwardian clothes for hanging out or hitting the clubs but switched to leather for brawling or for also hitting the clubs.