By chance I read up on the Essex Saver (£11.10 for a day, except Sundays and bank holidays*) and was intrigued to find it is valid on applicable TfL services; AIUI non-TfL tickets aren't otherwise accepted on the London bus network. It looks like there's only one LSP route it's accepted on (NIBSbuses 269) so that may be the reason.
[* On those days, there's a Sunday Saver for £5.18 to reflect the service frequency. TfL routes that link Essex settlements a fair distance from the county boundary are specifically excluded, and those that enter Thurrock borough only (for Lakeside etc) are already beyond Saver validity.]
[* On those days, there's a Sunday Saver for £5.18 to reflect the service frequency. TfL routes that link Essex settlements a fair distance from the county boundary are specifically excluded, and those that enter Thurrock borough only (for Lakeside etc) are already beyond Saver validity.]