This is Psychoville, a BBC TV series created by Reece Shearsmith and Steve Pemberton (two of the creators of The League of Gentlemen)
The main character was a clown who performed at birthday parties.
There was another clown, who stole the main character's name.
Another character was an old, rich, and blind man, who lived in a mansion.
There were also two twin sisters, each missing one eye.
The Crabtree Sisters
The characters all wanted to get an alligator Beanie Baby doll that had survived a plane crash.
Both the old man and the twin sisters sold their eyes to buy the doll.
Lomax only needs one more item to complete his collection, Snappy the
Crocodile. He once discovered it online, but two more people, the
Crabtree sisters (conjoined twins from Braintree, Essex) bought it
before him. Lomax bought Snappy from the sisters in exchange for his
I believe the series was a sequel to another earlier British series.
Not really a sequal, but I suspect you are thinking of The League of Gentlemen
See also Wikipedia and BBC page.
The series revolves around five different characters from different
parts of England: David Sowerbutts (played by Pemberton), a serial
killer-obsessed man-child who still lives with his mother Maureen
(Shearsmith); Mr. Jelly (Shearsmith), an embittered one-handed
children's entertainer; Oscar Lomax (Pemberton), a blind millionaire
who collects stuffed toy animals; Joy Aston (French), a midwife who
treats a practice doll as if it is her real child; and Robert
Greenspan (Tompkins), a panto dwarf in love with his Snow White who
believes he has the power of telekinesis. All five are connected by a
mysterious blackmailer who has sent them a letter each with the
message: "I know what you did". The series is named after the title
given to The League of Gentlemen when the series was sold to Japan and