So, yet again, do you know that IEP will be narrower (than Mk3s etc), or are you just not a fan of fat people?

No but simple geometrical laws apply. If the vehicles are not narrower, and I have seen a figure of 2.70 given (the same as the slimline class 158), either the route availability of the 26 metre vehicle will be very restricted and/or a fortune will have to be spend on changes to the infrastructure.
Mark 3 stock also has the advantage of very thin sides due to the constructional system used, top hat sections welded to the sheet metal of the bodyside. Nearly all modern stock seems to be extruded aluminium which is inherently thicker and incidentally has little weight advantage either.
To avoid overthrow on curves, the width must be reduced from the maximum of 2.82 by an amount proportional to the square of the distance between bogie centres, and there are corresponding requirements for the outer ends. The 2.82 width figure applies to vehicles with a bogie spacing of 14.17 metres. Mark 3 stock is 2.74 metres wide with a 16 metre bogie spacing. This was the same width as mark 1 after allowing for projections such as door handles. Later 20 metre stock is built to the full width of 2.82 eg classes 455, 375, etc, which gives a reasonable amount of space for 2+2 seating.
The specification for IEP should have required a width of not less than 2.80 which would permit a vehicle length slightly more than 20 metres. But hey, it doesn't really matter because first class seating will be 2+1 and why should anyone care about the oiks who travel standard class?