Nope.
After they adopted the Beesley action, Purdey also made Best-quality sidelock hammerless shotguns on Rogers-patent actions. The Rogers is a standard-style action that cocks when the bbls drop. It is not a self opener.
W.C. Scott and Webley & Scott used this action on their hammerless sidelocks. I believe Purdey bought their Roger actions in the white from Scott and finished them off in their London factory.
Of course, Purdey also made hammerguns - bar action, island locks - well after 1880.
After 1880, Purdey also made boxlocks on A& D actions and B & C quality sidelock hammerless shotguns on non-Beesley actions. These lower grade guns were made into the 1920s.
Here's a pic of one:
http://www.doublegunshop.com/boston/bs_purdey-10488_0103.jpg(BTW: that's not a Best-quality gun, regardless of what the dealer claims.)
Say hello to Ginger and Mary Ann for me.
OWD