Our elections office are happy to provide an estimate for the cost of an election at a time other than when the full district elections take place. It is horrifyingly expensive! At the last count, we were quoted something in the region of £7,500 but that was a couple of years ago and that's per election so if just one person resigns or leaves and there's a call for an election, that's what they propose charging. God forbid if more than one resigns at a separate time and there's a call for another election! However, we do have an electorate of 3,000! For an uncontested election (but note, election not co-option) it's £500. I think it depends on your principal authority.