A new captain will be announced next week but Barden's decision has opened the way for former skipper Andy Vilk to be named in a 14-man training squad.
Vilk, the former Northampton and Sale flanker, has been training with England's Sevens squad this season while also playing under Neil Back for Rugby Lions.
With Christian Lewis-Pratt to undergo shoulder surgery, England coach Ben Ryan has included the uncapped playmaker Dan Bibby.
England are currently fourth in the world series table but looking to round off a disappointing season with victories in Glasgow next weekend and at the Marriott London Sevens on May 12-13.
Last year's London leg attracted a crowd of 100,094 over the two days.
England Sevens: Dan Bibby (UWIC), John Brake, Chris Brightwell, Chris Cracknell, Isoa Damudamu (British Army), Sam Edgerley (Rosslyn Park), Simon Hunt, Tom Mitchell (Oxford University), Dan Norton, Tom Powell, James Rodwell, Mathew Turner, Rob Vickerman, Andy Vilk (Rugby Lions).