The parties all have meetings of their MPs which provide an opportunity for the party leader to put across what they are doing and answer criticisms. It can also be a means of letting MPs let off steam and allow the leadership to head off a revolt. 

For the Conservatives the 1922 Committee is the main body, previously only consisting of backbenchers but the rules were changed in 2010 to allow ministers to be involved and, for Labour. The Parliamentary Labour Party and the Liberal Democrats also meet as a group.  

These groups, especially the 1922 Committee, can also act as the focus for rebellion though. John Major, fed up with criticisms of his Government at 1922 Committee meetings, decided to call a leadership election to clear the air. Peter Bone and Christopher Chope as members of the 1922 Executive kept up a running criticism of the Coalition until voted off by newer MPs in 2012. 

The PLP elected the Shadow Cabinet when in Opposition and so could be an alternative centre of power to the leadership. This was ended in 2010 but the PLP has been a centre of criticism of Jeremy Corbyn’s leadership of the Labour Party.