313 desperately needs a refurbishment. I like the Southern idea, as their 313s feel much more spacious, have better interior design and always seem to be cleaner.
I'd have the 313s, along with 314s, 315s, 507s, 508s, 455s and 456s, as one of the sacrificial classes to be replaced by the new Standard Local EMU. It would also run on Crossrail. It might simply be a 378, or it might be something new, but it would be a simple design, presumably available in 3-car and 4-car versions, possibly overhead, 3rd-rail or dual-system. All versions would share several features. Plenty of seats, but also room for standing and at least one toilet per unit. Other than that, not much else.
Basically, this would do what the PEP-based units and the Networkers were supposed to, produce a standard EMU for local trains.
I'd also start thinking about a diesel version to replace Pacers.
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The 365s ought to have air-conditioning fitted.
Please don't, I'm glad there's still one train where you can get a decent feeling of air movement and that doesn't turn into an oven when an electrical fault happens (or the power goes off, which is worse).