1951 Rudge Aero Clubman

The bottle holder on this bike is vintage, you can find both old and modern ones on ebay just search "handle bar bottle cage". Vintage ones will cost you around 40 bucks modern ones around 10. You can also find adapters for standard bottle holders.

The racers back in the 40's and 50's used to use them, often double ones. I don't know exactly when or why they quit, I imagine for aerodynamic reasons. Also they have to hold the bottle pretty tight to keep it from jumping out on bumps. Many of the old ones have a lever that tightens the cage on the bottle.

I think that's actually a water bottle holder. But it raises an interesting question: How well does an insulated coffee cup fit in a standard water bottle holder? You can get handlebar clamps for regular water bottle cages.

There are aftermarket coffee cup holders branded by SOMA, Felt, Topline and Origin8, among others.

EDIT: Well, I'll be damned! OXO 12/14oz Travel Mugs fit a standard bottle cage very well. I have a couple of these: A nonthermal version that comes standard with the SOMA Morning Rush kit, and a thermal stainless steel one that has a better sealing top. Both of them fit Elite Ciussi bottle cages very snugly. That means you could toss your coffee mug in your downtube cage, or you could get a handlebar mounting clamp for a standard cage. Excellento!

Further investigation suggests that the water bottle holder on the handlebars is French - a Specialites T.A. ref. 213. T.A. made lots of stuff for touring bikes: Cranksets/chainrings/BBs, racks/bags, bottles/cages, pedals/cleats, headsets and so on. Very rugged stuff. They're still in business, and they still make the six-arm cyclotouriste crankset they've made for almost 50 years.