I was thinking about it the other day and obviously to take into account boundary changes the figure varies. A strong contender, I think would be my own Hamilton. There was a by-election in 1943, 1967, 1978 and again in it's succesor seat of Hamilton South in 1999. But going back to say 1918 or 1900, there must be some constituency and its successors that has had more than 4 by-elections (I'm thinking Northern Ireland in particular, Mid Ulster had 3 elections in 1955-56, the General Elction and two-by elections IIRC due to problems with the candidates' eligability).
Any idea's ?
EDIT: Mid Ulster also had 4 by-elections
They had another two in 1969 and 1986.