My parents had told us of their family history. According to my father he was descended from the man who founded Calcutta (now Kolkata). (that person was named in one of the specialist rounds of Mastermind). An interesting fact about that man is that whilst there he heard of a woman whose husband had died. The practice at the time was suttee where the widow sacrificed herself on the husband's funeral pyre. He stepped in to save the woman and married her. That was the source of the story in Jules Verne's Around the World in 80 Days.
There's just one problem with the story of my father being a descendant. The man and Indian woman had 3 daughters who did go on to marry and 1 son who didn't survive to adulthood. We don't have that man's surname and I did find an old family bible where a woman with his surname is mentioned. So although it looks as if an ancestor married a woman whose father had the surname but cannot have been a direct descendant of the man who founded Calcutta.
According to my mother, her family could be traced to pre 1066. A man from Normandy had settled here, and acted as a spy form William the Conqueror. After 1066, William gave him land as reward provided he became Christian, having been Jewish. My mother knew his name. There's just one problem. He's not mentioned in the Domesday Book.
It is possible to trace my mother's family several hundred years. The only mildly interesting ancestor is a lithographer who was based in London. He introduced the artist James Whistler (of Whistler's Mother fame) to lithography. My ancestor had a son who was also a lithographer, amongst his work were posters for the London Underground between 1910 and 1913.