Up to and including the 1992 tube stock (so not the 1995, 1996, 2009 tube stock, and S stock) virtually all 'full length' London Underground trains were splittable into separate 2, 3 or 4 car units, which normally worked in multiple (to make 6-8 car 'full length' trains), but which could be uncoupled, and - provided that they had an operational cab at each end - worked separately (as short trains); otherwise such units were - on their own - restricted to shunting manouvres, within depots. and to attach to 'short' trains in stations. Up until the mid 1970s the Underground had a practice termed 'uncoupling' - shortening trains outside peak periods, by detaching units. Exception were the 9-car trains used on the Northern line, where each car had a special position in the 9.
In the earliest days it must remembered that stock was all essentially individual cars, coupled to form trains as required. Then there was a move to semi-permanent units, with cabs at each end: on the tube lines standard unit from the 1910s to c1930 was an M-CT (motor & control trailer), generally with an intermediate trailer, forming long, six car, trains M-T-CT+CT-T-M which would be split to forma three car units off peak; or sometimes with two car (M-CT) units for off peak. Eventually, with the standard stock from c1930, seven car trains M-T-T-M+CT-T-M were formed - I think it was unusual for the three car units to work on their own. And different lines had different formations & practices.
Subsequent stock was formed into much more permanent units. The 1935 (prototype) stock was formed in M-M pairs; the earlier 1938 stock was (normally) M-NDM (non-driving motor)-T-M+M-T-M seven car trains (but AIUI, 6 or 8 car trains could be formed; and again AIUI the normal 'short' train was 4 car, but could have been 3. Later, UNDM (uncoupling NDM - which did have a controller cabinet, for use when shunting) cars wer built, to form UNDM-T-M three units, which could only work coupled to a four unit (M car at each end). Subsequent tube stock - up to the 1983 stock was similarly formed of three or four car units (variously with cabs at one or both ends - and some cabs were later decommissioned), coupled as required, but which could be split (and, with cab at both ends, work separately). The 1986 and 1992 stock came in two car pairs, assembled as required - some of the 1992 pairs did not have a cab, and could only be used in the middle of trains.
Surface stock was similarly uncouplable, but on a more varied basis.