Green’s Dictionary of Slang

Clerkenwell, London EC1, thus Weller, a local inhabitant.

1895

Mirror of Life 26 Jan. 3/1: Kt is well that Clerkenwell has been the birthplace of inumerable celebrities [...] considering how much the ‘Well’ has lost [...] The ‘Wellers’ did not have these cages [i.e. local prisons] to themselves.