There are non-trivial numbers of diesel-mechanical (IC to wheels via a gearbox) and diesel-hydraulic (IC to wheels via a fluid coupling) trains out there. The British class 172 Turbostar is an example of the former, most other class 1xx DMUs the latter.

Diesel electric transmission does happen on smaller multiple units sometimes, but really shines on larger and faster trains, or on electro-diesels (where you need the electric final drive anyway).

Doubt Farringdon switched from diesel to overhead - overhead to third rail. Some trains have to stop to raise the pantograph, some do it on the fly (I think the 395s can switch 3rd rail to ohel at 60mph when coming on/off hs1)

Some trains are hybrid - will use electricity while under wires, and switch to diesel when there's no wires, the new class 800 in the UK as an example.

It was diesel to overhead. It was the Thameslink train and I think it used diesel south of London (to Brighton).

When the snow hill tunnel re-opened in 1988, and trains started from Farringdon to Blackfriars, they were operated by class 319s, which were dual voltage from the very start. While I'm sure some diesel engineering trains have been through the tunnels, and perhaps some diesel goods trains in the 60s before the closure, I'm not aware of any diesel passenger trains through them (as there were no passenger trains since 1916)

Some 319s are being converted to partial diesel and becoming class 769s, but not on this route.

Oh it could have been switching from overhead to third rail... I never actually went on the train to Brighton, I just remember the pantograph coming down.

Still does it now, there's a similar switchover north of Shepherds Bush. The Southern 350s used to stop when I got that train, I think the overground trains can raise/lower on the fly. I assume there's a similar changeover in East London.

Before 2009 and HS1 to St Pancras, Eurostar also switched from overhead to third rail, on the fly I think, somewhere near Ashford.

You're completely wrong. Most diesel locomotives are in fact diesel electrics. I.e. diesel engine, generator, electric motors. Most of those cannot use external power sources (although a few can, e.g. class 73 in the UK).

Certainly in the UK: the most common locomotives such as class 66, 60, 58, 67, 47 - they're all diesel electric.

In the US, same story: for passengers the GE Genesis is pretty big, things like SD90MAC and AC6000CW are big for freight.

I think you misread my comment.