I've never really considered the 350/444/450s as being based on any prior UK-design. I thought they were just the Siemens Desiro, tailored to UK requirements with end-gangways stuck-on.
Are they actually based on a previous UK design such as the 309 or 442 or is it simply they bear a similarly to previous designs?
Although not officially, arguably with mainly modern features however desiros do contain features that do give a nod to the slam door trains (such as the class 411, 412,421,423, that came before the them) that the desiro types replaced
such as
the doors slamming
the cab ends how they have a similar shape
the end gangways (although with no window)
the 3+2 seating arrangement which was based of similar seating arrangement in the slam door era
I know from the way they look, (the 444 Being the most different) they dont look like they have anything compared to the slam door trains before but when you think about the individual elements you can see how some trains are similar to the stocks they replace even if not “officially” based off them