By late 1950's the original teddy boys were no more, broken up into various sub cultures, most fell by the wayside but two major groups remained and grew from the ruins of what was once the Teddy Boys to become the "Ton Up Boys" and the "Coffee Bar Cats"...
The "Ton Up Boys", were those teddies that had held the motorcycle and American Rock'n'Roll as their foundations and now wore leather, big boots and rode British machines to and from various road side cafés.
The "Coffee Bar Cats" aspired to a more Latin look, and their neo Italian style appreciated modern jazz, ventless thin lapelled box suit jackets and they chose Italian scooters as the superior mode of transport for such well dressed Cats...
It's not hard to figure how these late 50's early 60's sub culture's and indeed underground fashions grew into the Mods and Rockers of the mid 60's.
The Coffee Bar Cats felt they were the modern movement and the Ton Up Boys represented all that was gone and should remain buried in a pile of dirty bikes and dirty leathers. Hence as they grew and needed to encompass all their new members, they eventually termed themselves the Modernists and the Mods were born.