My brother and I have both been posting on this question. I used to own a Charles Lancaster 16 Bore double rifle on the same Purdey's patent thumbhole action. It was made in 1875 and was cased with all accessories. It had in gold on the rib " Made for the Maharaja of Bulrampore, Odah 1875" and looked very similar to your rifle, only with oval bore rifling. A very similar 16 Bore double rifle that was fitted with ivory accessories and gold washed sold recently. It was a Rodda and was a Purdey thumbhole also. I believe Puglisi Imporium had it for sale.
That is a really nice rifle you have.
My brother and I mostly have Alex Henry double rifles and none of the ones we have owned have had a serial number less than 2400. All were made later than 1872 per the Alex Henry records. I can e-mail you pictures of the Bulrampure rifle if you want. Take care and good luck.