Lord London was a title in the hereditary peerage of England that was held by several people on Earth. During the 22nd century, it was given to at least two people, the most famous of whom waged a long and bitter war against Lord Haldoran.
22nd century history
Donna's father
One Lord London had a daughter named Donna. Along with the Eighth Doctor, he waged a war against Lord Haldoran and the Master.
Some time during the war, this London gave his seventeen-year-old daughter to Haldoran to marry to create peace. Haldoran tortured Donna and constantly attempted to impregnate her, until she was found infertile. He divorced her and took her cousin, Brittany, who bore him twelve children.
London shunned his daughter after learning of her infertility. He allowed her to go off and become a knight, yet thought of her safety in his last battle.
London was killed when one of his own men shot him for bargaining in a surrender. Little known to him or his men, Haldoran had been killed by Donna moments before.
Toby Barlow
After the death of Donna's father, the previous Lord London, the Domains Haldoran and London were combined under a new Lord London, originally named Toby Barlow. He had been on Haldoran's council, and emerged as the most likely heir to both titles once the previous Lords Haldoran and London died fighting each other.
He also eventually married Donna, and joked during his marriage proposal that it was merely going to be a marriage of political convenience. Since she was the daughter of the previous London, it could only help cement his claim to the title. However, after they had been married for a while, Donna told the Eighth Doctor that Toby, Lord London, had lied when he said he was not marrying for love. (PROSE: Legacy of the Daleks)
Behind the scenes
The way in which this title passed down was never made particularly clear by Legacy of the Daleks. It seems to have worked differently than aristocratic succession at other points in English history. A part of this may be down to the fact that there is no sitting English monarch. Indeed, the battle between London and Haldoran is really for the throne of England, not just control of New London. This lack of central authority may explain why the title seems to revolve around both inherited right and brute force.
A particular mystery is why Donna dosn't just become "Lady London" on her father's death.
The Doctor surmises on first meeting Donna that she might be disinherited, yet she is still welcome, even expected, in her father's house, and she still retains her title of knight. So if she's been disinherited, it's been done in a peculiar way.
Moreover, if titles are skipping females in the 22nd century England, this would represent a considerable change over the way things had been done in earlier centuries. For instance, the Tenth Doctor tells Donna Noble that Lady Clemency Eddison possessed the title, "Lady Eddison", in her own right. In early 20th century England, aristocratic titles, though not monarchical ones, passed to the first-born child, regardless of gender — at least, according to TV: The Unicorn and the Wasp.
Of course, she does become "Lady London"; it's just that the book doesn't particularly clearly lay out why she needs to do it through marriage.