This week we at last reach dukes, the highest rank short of royalty in the British peerage. (I'm going to leave royal dukes out of it, because A) the Wellington and Denver dukedoms that are the subject of this series aren't royal, and B) they're not generally an issue in fiction, because most authors of, say, Regency romances aren't going to create fictional royal dukes.)
The first thing you need to know about dukes is that they're rare. Currently there are only twenty-seven extant dukedoms in the British peerage (you can find a list of them here). To become a duke, in general you either needed to be an extraordinarily influential and powerful aristocrat...or else have the good fortune to be Charles II's bastard son. (He created the Dukedoms of Monmouth, Richmond, Lennox, Southampton, Grafton, and St Albans for his offspring.) The closest thing to merit-based dukedoms that I know of are Wellington and Marlborough, and it's not like the first holders of those titles were of anything approaching humble birth.
Dukes, being a cut above the rest of the peerage, are addressed differently. They are not called "my lord," and if you encounter a reference to "Lord Wellington" in a novel set during the Waterloo campaign (i.e. after he was granted his dukedom in 1814), the author missed that detail. If you someday have the chance to, say, travel in the TARDIS to observe the Battle of Waterloo (a fantasy of mine, I admit), you should address Wellington as "Your Grace," unless you feel yourself to be on familiar, equal terms with him, in which case "Duke" or "Wellington" would be appropriate. Or "sir," but in the "Yes, sir" sense, not the knightly one.