The Treasury Select Committee is unlikely to hold an early inquiry into Lloyd's, according to senior parliamentary sources.
A Labour Party source on the committee in the last parliament said she would be "gobsmacked" if an early investigation was launched.
Last week John McFall, the last parliament's Treasury Select Committee chairman, was seen at Lloyd's, prompting speculation that he would inspect the market.
But the committee source said a Labour-dominated committee would have "other priorities".
' John McFall is expected to continue as chairman of the Treasury Select Committee.
One Labour member of the committee in the last parliament said she would be "very surprised" if McFall were not chairman again. And a whip said he was sure McFall would carry on in the role.
McFall, the MP for West Dunbartonshire, refused to confirm whether he would stand again. He said it was "too early" to discuss the make-up of the committee.
The chairman is not expected to be chosen before the end of June.