How the characters in Look Back in Anger influence each other is a very interesting question. Some critics might argue that part of the existential dilemma of the play is that they don't influence each other--they only torment or tolerate each other. Although it may be said that Jimmy has an influence over Colonel Redfern because Redfern comes to agree with Jimmy's point of view about the Colonel being obsolete.
Jimmy's influence over Alison seems to be restricted to depressing and worrying her. She is upper class and was brought up in the complacent comfort of assumed and realized privilege. Jimmy married her for the comfort her composure afforded him--the composure he rails at in their married life. The chief influence Alison seems to have on Jimmy is to drive him to irritated ire because she doesn't feel, she doesn't have strong emotions for anything. This is shown in her complacent action of ironing on Sunday evenings.
Cliff seems to have somewhat of a calming influence on Jimmy. Who knows what he might do if Cliff weren't there telling him to be quiet and leave Alison alone. At first Helena has the same influence on Jimmy that Alison has because they are both upper class and proper and both have religious church affiliations. After Alison leaves, Helena confesses her love for Jimmy and they start an affair--which comes to look exactly like the relationship Jimmy had with Alison.
There is much debate as to why this is so. Does Helena take quietly to the passive ironing board out of enforced sexist expectation of the female role? Does she do it because that is the only option for an upper class woman suffering under the invective of Jimmy's class system hatred--a silent retreat into passive activity? Is it because of the class system definitions of roles, which would be ironic because it is the class system that Jimmy hates with such a passion?