Sid â€” As you say, almost certainly either Davidson or Greener Pearline, although Pearline should really only be applied to Davidson. Convention today is to use the initial capital tradename for Davidson, the lowercase generic term for Greener and other manufacturers. Davidson's patent for Pearline was approved Dec. 7, 1889, see http://www.cloudglass.com/Patents.htm
I prefer a Greener attribution for this pattern as there are Greener registered designs with similar flamboyant gadrooning but with different main body patterns, like 138051 of Nov. 14, 1889. In fact your posy basket could be covered by this particular registration as several Greener registrations around this time were of components of patterns, not the whole design.
One further thought. If anyone knows of an example in amber pearline, that would substantiate the Greener attribution, as amber pearline was only made by Greener and Molineaux & Webb to my knowledge, not by Davidson.
It is nice to see your supplementary on auctionbytes at http://www.auctionbytes.com/forum/phpBB/viewtopic.php?t=14466
I have taken the liberty of posting a link to this topic so that readers can see what I actually wrote in response to your query.