Mississippian,

Some information on Henry W Egg that may be of interest and assist in dating your double.
Egg, Josef (brother of Durrs) 1780
1816 1 Piccadilly London
1838 sons Charles & Henry trading as Egg & Sons. (they bought the lease and business of Joseh
Manton & Son and advertised as 'successors to J.Manton & Son)
1844 Charles & Henry Egg
1851 Henry Egg
1870-1880 Henry William Egg

It would appear that the business did not exist after 1880.
Henry's uncle's business 'Durs Egg' ceased business in 1875 when it was taken over by Watson.

That is a classic double by a top maker well spotted.
Hope this helps.
Fraser Double