I have pictures of the shotgun on Gunbroker if you care to have look.( Gunbroker.com Item No.461801479)
They are indeed Birmingham proofs on the barrel. The D. Egg engraved on the lockplate is identical to some others I have found on the Web. Gunbroker.com Item No.461801479
Here is info from another forum concerning the Gunmaker:
Boothroyd's Directory lists Durs Egg's death in London 1831 but states the business continued under that name until 1865, so a percussion gun may date later than 1830s. Here's a percussion double for comparison:
http://www.littlegun.info/arme britannique/artisan efg/a egg gb.htm