I think posh mid- late 50s, without trying to go by my black and white pictures!
Here as some little snippets from the book credited above in my previous post, which probably aren't relevant exactly but may be useful in future:
"In the 1930s rayon appeared as a substitute for silk in umbrella covers, rather later than it had first been used for dresses."
[After a fluctuating fashion between long and short in women's umbrella's post WWI]
"The walking length umbrella returned to fashion towards the end of the 1930s. A small-rolling 'pencil slim' umbrella with an ivory 'thimble' top appears in the Barker's catalogue for 1936, and the Army and Navy Stores offers a 'new walking length' of 33 inches in 1937... In June 1937 the French magazine Marie-Claire reported; 'At Lobb's, they told me of the demise of the Tom Thumb, the stout little umbrella which we have loved for so long'. "
(OK bored of quoting now as I am a terrible typist so shall paraphrase instead :D )
Late 40s into the 50s (New Look) it appears that the long, slim umbrella was still in fashion, typically with plain or checked covers.. Stout, masculine handles continued into the 50s, then ran concurrently with slim straight handles into the decade.
In the mid 50s a few eccentric novelty type handles appeared. Many of the slim rolling umbrellas are on metal sticks - the long thin hooked handles in marbled plastics, or leather dyed to match the cover, appear at the end of the 50s.
America had nylon covered umbrella's shortly after the war, Britain probably in the early 1950s.
In the 1970s (as you would expect with lots of hippies) about there was a call for return to nature with materials that were more environmentally friendly to produce. Stout wooden hook handles and bright cotton covers by the mid seventies, novelty duck head handles in 1975 (incase you wanted to pin that one down :P )!
So there you go. I do halfheartedly collect (accumulate) umbrella's but sadly am not an expert. I had real trouble finding a reference book, and this is the most detailed I have come across. Trouble is it goes into more depth about the previous centuries too, so while still being very useful I am still on the look out for a book about the umbrella solely in the 20th century. So if anyone can recommend one let me know!