508 and 455 had power jumpers. 507 didnt, because they worked underground single bore tunnels. When 508 tranferred to Merseyrail, the were removed. later 507 and 508 had them installed. As far as aware all southern emu had them fitted. EPB, CEP, CIG, REP, and so on.
others have answered in between, but I think in general you are confusing
inter-unit and
intra-unit power jumpers. (I'll stick with the term jumper albeit not exactly the correct one).
units for working in tunnels /generally/ have no
intra-unit jumpers i.e. each motor coach is /generally/ isolated from the other; when on DC 313s as built for Moorgates were all like this; when on AC as they were above ground and electrically coupled via the middle (transformer) coach; when some went to NLL etc a mod was done (to make them 313/1) that interconnected the two motor coaches within each unit.
508
as built and 455 had
intra-unit jumpers - but never
inter unit; no modern unit has, as has been posted here already, the last squadron fleet with
inter unit power jumpers were 4Sub, initial 4EPB did but removed very early on. Every other main line unit I can think of (but see long units below) had
intra unit jumpers.
Having said all that, there is a common myth that underground trains are not permitted intra-car power jumpers at all; this is not true, 1992 tube stock for example every car is a motor coach; there is one shoe set per pair of cars, traction does jump one car (with shoes) to the adjacent car (no shoes); what is not allowed is to daisy chain those pairs together. there are similar configurations on S stock.
Long units like 700s have no complete through
intra-unit traction link; the two halves of a 700 - both 700/0 and 700/1 - are w.r.t. traction power, AC or DC, isolated from each other; one half fails it is dead, the unit is on half power; there is of course auxiliary / control power through the whole unit. The effect is a 700 is more or less two discrete coupled units. AIUI 345s and 10car 701s are similar but I don't know where the breaks are, if any; I assume a 10.701 is split symetrically 5/5, and a 9.345 split either side of the middle car that happens [or deliberately] to be a trailer. Anyone know for sure ?
I am not sure 444/450 diodes is correct; it is true they were not permitted to regen in their early days but IIMU was simply blocked within the traction pack software. TBH I had never heard of diodes used here before, it might be right, just saying I never heard of this before, nor do I understand why it would be needed when s/w blocking could do the same thing.