The tambour (alternatively: Napoleon's hat, humpback, naval, or even cathedral clock) began as an American development of the so-called 'drumhead' mantel clock. The earliest examples I've found examples of were made by Bawo & Dotter (Charles Jacques) during the 1910s and usually incorporated chiming movements. By 1923 seemingly every American clock maker had some variation of the tambour and began incorporating different styles into the mix. Unfortunately the economic depression of the 1930s cut into the American clock market, heralding the end of the higher-end fare. The style never really died out but later American tambours are but a mere shadow of what was once popular.
Concurrent with the tambour was an upright mantel clock commonly known as the beehive. It is basically the same as a tambour except for its upright shape and was often modeled after a cathedral arch, going with the once-prominent Gothic revival style.
In Britain, the tambour made its way by the 1920s. I don't think any particular maker was responsible for its introduction across the pond - they all basically jumped in on the style at once. On average, British tambours tend to be smaller than their American counterparts but there are exceptions to this.
While production of tambours would survive up to the 1960s, many later ones really take on a sort of 'honey bun' shape largely influenced by art deco or even space age styling. Conversely, upright 'beehive' mantel clocks do not seem to be so prevalent in Britain.
Because the tambour was long seen as a modern clock, little existing publications have bothered to document its development.
Out of a sizable number of tambours I've documented, here is a nice one from the Geo. Borgfeldt & Co. 'Celebrate' brand. Also shown is an upright mantel clock from the same line. Both are from the 1927-1933 time frame.
The Cuckoo Clock Mfg. Company sold large numbers of Tambour clocks with good-quality German movements under the "Necor" and "Linden" brands until the mid 1980s. Perhaps not higher end, but worth consideration within the context of a timeline.