Classic Bulldog names reflect both the homeland of the breed - England - and the character of the dog - stodgy and dignified.
These names should carry a sense of class and Englishness. This can sometimes also appear ironic because while English Bulldogs may look dignified, any English Bulldog owner will tell you that they sure don't always act that way.
For Male Bulldogs
Winston - after Sir Winston Churchill. A truly classic name.
Thurston - remember Thurston Howell from Giligan's Island?
Bentley - very English name with the added cachet of the expensive car.
Edgar - with a nod to J. Edgar Hoover, who looked like a bulldog.
Henry - a very royal English name.
Sir (Insert Name) - any old name sounds more English Bulldoggy if you put the word "Sir" in front of it. Sir Jake, Sir Remington, Sir Raul, whatever. You can also do the same with titles like Lord (Insert Name), King (insert Name), you get the idea.
Angus - User submitted this great male bulldog name.
Barkley - dogs bark..get it? Adding "-ley" to something always makes it sound more British anyway.
People have also sent in very English sounding bulldog names like Baxter, Belvedere, Benson, Bewster, Archie, Alfred, Arthur, Humphrey, Alestair, Sherlock, Malcolm, Spencer, Jeeves, and Onslow. Onslow is great if you were a fan of BBC's Keeping Up Appearances show. Oxford is another good submission (Ox for short).
For Female Bulldogs
Lady (Insert Name) - just like with "Sir" for male bulldogs, female bulldogs can be named Lady Diana, Lady Jane, Lady Betty, Lady Kate, etc.
Margaret - in honor of Margaret Thatcher, the first female Prime Minister of the U.K. Also, you can call her Maggie for short.
Gertrude - such a fit.
Lovey - how cute yet English can you be at the same time?
Emma - a great old Anglo Saxon bulldog name.
Audrey - a classic, classy name for a classy gal bulldog.