As to the steam days, which were before my time, I have a question; The steam engine came up to the concourse, did they drive them backwards towards Windsor, Portsmouth etc. or did another engine come along and connect to the other end? @davesgcr and other train nerds...
as far as main line engines are concerned, after coming in to waterloo from (say) bournemouth, they would go 'tender first' to nine elms depot where they would get another load of coal, then they would go on the turntable, thus-ish -
then run tender first to waterloo and take another train out.
depending on circumstances, either a shunting engine would remove the carriages (so they could be cleaned, and the bog water tanks re-filled) to release the loco, or the arriving loco would have to wait until the train departed.)
waterloo did have a turntable - see
1951 OS map - but it looks possibly a bit small for a full size loco, and was probably only used by locos on suburban trains (most of the inner suburban lines from waterloo went electric between the 20s and the 1939 war)
'push pull' operation of steam trains (where the train was driven from the front but the loco was still at the back) was restricted to quite short trains on branch lines, as in this example on the westerham branch
even in to the BR diesel / electric locomotive era, push-pull operation was quite a rarity, it was used on the bournemouth-weymouth line from the late 60s, when they electrified only as far as Bournemouth -
the diesel loco here is pushing the un-powered trailer set, the driver is in a cab in the front carriage. the un-powered bit was pushed from waterloo to bournemouth by an electric unit.
full on main line push-pull operation didn't really happen in the UK until the mid 80s on the Glasgow-Edinburgh line.