Only the deep level tube lines have small carriages due to the small tunnel bores which are much farther underground than those in NYC. Despite being smaller in profile they have the same 1435mm track gauge as mainline UK and US trains. The shallower "cut n cover" or sub surface lines are much the same size as NYC subway trains and mainline UK trains. The deep level lines are: Northern, Central, Victoria, Bakerloo, Piccadilly, Jubilee and Waterloo and city. The others (Metropolitan, Circle, Hammersmith & City and District) are larger trains in terms of loading gauge but not necessarily length. Central line trains are 8 cars long but the "larger" circle line trains are only 6 cars long. The DLR is in a class of its own. Somewhere between the smaller and larger trains it is formed of 2 car units in multiples of 2 or 3, so up to 6 cars. They have no driver in the traditional sense but are self guided with occasional assistance from a human operator.
I don't think the Jubilee (or "Jubbly" line as many locals call it in reference to Only Fools & Horses) has any more signalling issues than any other line really. It may just be the perception from the program coverage. If there is LUL staff here they may be able to correct. me on that.