Replace internal wall with 6m RSJ?

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Hello all, i am looking at removing an internal wall and replacing with RSJ. The wall runs from one side of the house about 3m then has a 90' wall which is 900mm then another 90' so wall is parallel again with the first 3m wall. This second wall is around 2.7M. The wall is a single brick wall and the 2.7m part is 900mm (the width of the back door) away from the party wall. The 3m part is then 1800mm from the party wall. Neighbours have knocked down the 2.7M part with out any additional work. Apparently calculations say the beams are adequate for the span. The house was built around 1950's and we believe the wall is there simply to separate the passage way from the kitchen. The passage has a back door at one end and then a front door (not the main front door). I would like to know what size RSJ would be adequate for this? The wall in question does not continue through to the upstairs. The beams in the roof running directly over this wall are 175mm x 50mm. The span they would run if the wall was removed with no RSJ would be 3750mm. I have uploaded a few pics if this helps.
Any advice appreciated. I have been in touch with a structural engineer who is quoting me £300 to come out and advise. This is fine but I want other thoughts on this and any ideas before I have him visit.
The sketches show current layout, what the neighbours have removed, my proposed layout (not showing an RSJ) and the upstairs floor.
 

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