BBC News reports (with a curious illustration of feet) a case of twins who were separated at birth and separately adopted and who only discovered their relationship after they were married. Hence annullment.
This has a touch of Siegmund and Sieglinde about it, and reminds me of the question as to whether English birth certificates have enough information on them.
This is all hearsay – told to the House of Lords by a peer who heard it from a High Court judge – so take it with a pinch of salt.
LATER NOTE: I traced the quote to Lord Alton of Liverpool on 10 December 2007 in the House of Lords Hansard, Column 101.
(Via John Bolch in Family Lore)