Young orphan Esther Summerson (Anna Maxwell Martin) is brought to the High Court of Chancery by lawyer Mr Kenge (Alistair McGowan). There she's thrown together with two wards of the court, Richard Carstone (Patrick Kennedy) and Ada Clare (Carey Mulligan).
Both are caught up in the infamous suit of Jarndyce and Jarndyce, which brings nothing but ruin and despair to all it touches.
At the Chancery courts, the three meet other beleaguered participants in the case, including the eccentric Miss Flite (Pauline Collins), who lodges nearby with the peculiar, and drunk, rag and bottle merchant, Krook (Johnny Vegas).
They have another lodger, Nemo (John Lynch), a very mysterious figure. He's a law-writer by trade, but a self-destructive opium addict by nature. When Esther bumps into him, she feels a strange shiver of recognition.
Esther, Richard and Ada spend their last night in London with the Jellyby family, before setting off to Bleak House to live with their new guardian John Jarndyce (Denis Lawson).
They are astonished to find the Jellyby household running to ruin as a result of Mrs Jellyby (Liza Tarbuck) spending more time dealing with far-flung matters of philanthropy than the problems on her own doorstep. Esther sympathises with her daughter, Caddy (Natalie Press), who is at her wits' end.
Esther, Ada and Richard receive a warm welcome at Bleak House from Mr Jarndyce. There they are introduced to his friend, Harold Skimpole (Nathaniel Parker), a man who shirks responsibility for his actions, as well as the public-spirited Mrs Pardiggle (Roberta Taylor). She escorts Esther, Ada and Richard on a charitable excursion to the slum dwellings of some poverty-stricken brick makers. There they witness the death of Jenny's (Charlie Brooks) baby.
Later, Guppy (Burn Gorman), a Lawyer's clerk, declares his feelings for Esther and proposes marriage. But Esther turns him down, saying she could never marry him.
Meanwhile, the elegant life of the beautiful Lady Dedlock (Gillian Anderson) is turned upside down when her husband's lawyer, Tulkinghorn (Charles Dance), gets wind of a secret from her past. She recognises the handwriting on a legal document, and Tulkinghorn determines to find out the name of the writer.
Tulkinghorn's investigation leads him into the dark underbelly of London, where he discovers that the writing belongs to Nemo. But when Tulkinghorn finally tracks Nemo down, he discovers that the law-writer is dead...