Eagle's candidacy is likely to prompt protests in her seat in Wallasey, Merseyside, where the constituency Labour party last week passed a motion of support for Corbyn, with a message directly to the leader, bypassing Eagle.
Seasoned Labour operators believe the motion will be defeated, with most constituency delegates likely to back the leadership, but No 10 and the party's Old Queen Street headquarters are leaving nothing to chance.
Former minister Diana Johnson published an email which has been sent to Labour MPs, warning them that they will face a vote of no confidence in their constituencies if they support Prime Minister David Cameron's motion.
He wanted to change party policy at the Labour party conference in September by getting members to push through the motion, but opposition from trade unions and constituency organisers blocked the debate from going ahead.
Motions were sent in by unions and constituencies, welded together into "composite" motions expressing similar views, and then put to the vote.
Nothing was done about the anarchic system by which any constituency Labour party or trade union could get its pet motion on to the annual conference agenda.
Opposition leaders, who said the government sought to gerrymander new electoral constituencies, called on the government to resign, which would set in motion new elections.
Her own constituency Labour party wrote to Eagle on Tuesday to urge her to reject the motion of no confidence in Corbyn, saying the delegates at the CLP AGM on Friday had asked their MP to back the leader.
The anti-war motion, Composite 6, is to be moved by the Regent's Park and Kensington constituency party and seconded by Walthamstow.
Stella Creasy, the Labour MP proposing the motion with the Conservatives' Justin Tomlinson, said she had met one person in her east London constituency with nine separate loans outstanding from the same short-term credit company.
