The brief but colourful parliamentary career of the Tory Louise Mensch has formally ended with a bizarre tradition.

Because MPs cannot resign in the conventional sense, Mensch had to accept a "paid office of the Crown", a new job that disqualified her from membership of the Commons.

The chancellor, George Osborne, has appointed her to be steward and bailiff of the Manor of Northstead, one of the two posts that allow MPs to leave the Commons.

The job is a sinecure, with no actual responsibilities – the manor house itself is under a lake near Scarborough.

The previous holder of the post was Labour's Sir Peter Soulsby, who quit the Commons to fight and win Leicester's mayoral election last year.

The other position to which MPs seeking to resign can be appointed is crown steward and bailiff of the Chiltern Hundreds (Stoke, Desborough and Burnham).

The posts are filled on an alternate basis, so the next MP to leave will be given that role by the chancellor.

Mensch's decision to stand down to move to New York with her family will provide David Cameron with a difficult byelection contest in the marginal Corby seat.

The author, who writes fiction under her maiden name Louise Bagshawe, won the constituency from Labour in 2010 with a majority of 1,951.

But polling by the Tory peer Lord Ashcroft suggested Labour had a 15-point lead in the contest, a swing that, if repeated nationally, would result in Ed Miliband taking the keys to 10 Downing Street.

The Conservatives dismissed an internet rumour that the former England cricket captain Andrew Strauss could take advantage of the free time he now has available to contest the seat for the Tories.

A source said: "We are not aware of any truth in it."