An intelligent, hard-working inventor and engineer, Doyce is stymied by the slow, annoying ways of the Circumlocution Office. Doyce is a pretty straightforward shout-out to one of Dickens's many pet side projects – getting creative people the kind of intellectual property protection that would make copyright and patent infringement much easier to fight against. (Oh, yes, Dickens had a whole slew of advocacy and political causes aside from his writing career. That man was like the Energizer Bunny.)
Doyce plays into the issue in several respects. First, he's been waiting and waiting to deploy his awesome time-and-money-saving invention in England, where it would presumably totally benefit industry and thus the economy. But no go, thanks to the red tape of the Circumlocution Office, where no one cares.
Second, Doyce decides to go sell the fruits of his intellectual labor in Russia, England's rival. Now what the characters in the novel don't know, but its readers do (since the book was set about 30 to 40 years before it was written) is that England and Russia are now (meaning the 1850s) at war in the Crimea. The bureaucratic snafus preventing British soldiers from getting the stuff they need are so beyond horrendous that there are almost as many of them dying from disease, cold, and hunger as from the actual fighting.
And finally, Russia gives Doyce all sorts of medals and awards for being awesome – which England only does for military exploits, not intellectual achievements – a huge pet peeve of Dickens's.