I doubt Dunhill made M&W-branded pipes.
Mine is clearly a Dunhill, but with the M&W name on the case in gold. Dunhill is also visible as an impression in the leather on the outside and on a label on the inside.
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Beautiful pipe Craig!
As you say the key here is the presence of the word Dunhill on the pipe and case. This isn’t an example of a private label pipe, but rather Dunhill branded pipes made for a given retailer to sell to its customers (Barling did the same thing). It would be interesting to know if Dunhill continued the practice after it opened its own Paris store a few years after your pipe was made. I’d guess not. In the States Dunhill pretty ruthlessly cut off other avenues of distribution when their NYC store opened in 1921.