I guess the obvious is a bi mode 23m with 2 pairs of doors, gangwayed throughout like a 444
However I wonder if 4 car sets would be more useful, with perhaps some 3 car units (for London-Salisbury only, with a higher proportion of first class). Maybe would require slightly shorter coaches. (Can the South Western take 260m trains, or is it limited to 240m these days. I remember travelling in the past on a class 50 +12 mk2Bs on Exeter route, but most only had loco plus 10 or 11 coaches)
Ideally could also work Portsmouth-Salisbury-Bristol-Cardiff route, but the segregation of franchises would probably preclude this. Even though a common fleet might be beneficial for both routes.