I guess that this depends on the definition of "rare".
I have seen many birds which I would count as "rare" on my 321 UK list.
However, I would suggest that the rarest is the Sociable Lapwing or Sociable Plover which is actually endangered globally.
Sociable Lapwing
I have seen this bird on 4 occasions in the UK between 1990 and 2005.
Richard