Firstly, and most obviously, both novels are set in London. Dickens is rightly considered the supreme portrayer of life in the great capital, but Hornby is also, in his own Arsenal-centric way, a chronicler of life in olde London towne, especially that part of it inhabited by guilty, liberal-minded middle-class types. Another similarity is the foregrounding of social injustice. Hornby's characters (well some of them...) attempt to change their slightly-privileged existence and start to do more for the less fortunate members of society, and, just as Mrs. Jellyby in 'Bleak House' does, inflict harm on their own family in doing so. In fact, this idea of charity starting at home (literally, and not for the benefit of those who live there) is very close to the ridiculous projects of Mrs. Jellyby and the rest of the well-meaning, but deluded, do-gooders of Dickens' imagination, but in Hornby's case (seen throught the eyes of Katie Carr, a doctor whose marriage is falling apart and whose husband has consequently attempted to change his life by becoming more forgiving and altruistic), we are unable to dismiss these do-gooders; we see that our cynicism is stopping us from doing what is right and helping those who are less fortunate.
The key to the book is the question: what does it mean to be good? Katie believes that her job as a doctor makes her automatically good; however, the more her husband tries to do real good, the more she sees that she needs to put herself before other people. This is also true for her children, who suffer (materially, at first, and later on emotionally) from the projects of their father and his new-age business partner. Despite deciding to make a go of the marriage, the effects of the efforts to be good bear little fruit, and the family is arguably in a worse-off position afterwards than they were before.
Katie is selfish, but, it could be argued, she has every right to be. Are the middle classes obliged, simply by having become relatively affluent and successful in life, to give away their riches because other people are worse off? When charity begins at home, should it stay there? How would your kids feel if you decided to give their computer to the homeless shelter?
'How To Be Good' is typical Hornby. There is sarcasm aplenty, a vivid insight into the pettiness and viciousness of domestic arguments (which, more than once, are likened to a kind of sport or game) and people asking awkward questions at socially inappropriate times. The idea of what it means to be good is something that must torture those of us who have a little more than we probably need, and Hornby catches the tortured ruminations of the London mortgage belt superbly. The only slight quibble I have with this book is that although the story is seen through the eyes of Katie (the first time that Hornby has used a female narrator), I'm not sure that it worked overly well; there may have been no real change to the book if the roles of Katie and David had been switched, and I'm not convinced that the author managed to capture the female mind. Certainly, there were definite shades of the central characters (all male) of his previous novels. Still, this is only a minor point, and not even Dickens got everything right!
The book has one more parallel with 'Bleak House'; the issues, whatever you may like to call them, have no resolution. Chancery is not reformed, and Katie's life is no better than it was before. Although she decides to stay at home and work on her life (including making more time for herself), you are tempted to think that it may all be in vain. When, at the end of the book, she looks out of the window and sees "nothing", you can't help but wonder if she made the right decision in staying with her husband after all.