The Pressed Steel railcars were often coupled to a single trailer to supplement capacity. I recall them used on the Paddington-Hayes & Harlington and Greenford off-peaks. The first generation units had I think a towing capacity: I once saw a railcar shunt a coal wagon around Southall depot! However any trailer that any modern-generation units would surely have to be coupled to a control-trailer of some sort to allow driving?
The first generation DMUs could couple to anything with vacume brakes as they had screw couplings and standard brake connections. The parcels units were often used to haul one or two wagons, and had additional power to cope with it. Other types could haul stuff, but would be pretty sluggish and with anything like a load would likely be tricky in anything but good adheasion conditions or on a gradient.
The Pressed Steel 121s did have some Driving Trailers built which were basically unpowered and none gangwayed 117 DMSs. They were no different to any other DMU vehicle. The 121s having 300hp in a single coach could easily cope with the trailer, just as many other first generation DMUs did with 300hp for 2 coaches.
Second generation DMUs have the wrong couplings, either BSI or Dellner, and more importantly have electropnumatic brakes so could not operate the brakes on anything being hauled. They can be hauled, and in extream cases could haul, using a barrier coach or emergency coupling, but without continous brakes.
The Mk1 and Mk2 EMUs, the 442s and the 325s have drophead buckeyes so can couple to any buckeye or screw fitted vehicles. Most Mk1 EMUs though had high level air pipes only, so needed adapters to couple to other stock with conventional low level pipes. 442s and 325s have both, so can couple to anything. That's more for being hauled though. I don't think there is anything stopping a 442 hauling a coach or two, but I don't think a 325 could, I think the brakes are set up just to allow them to be hauled (I don't think the driver's controller operates the westinghouse brake, just the EP). Like the Parcels DMUs, I think the MLVs were the only ones ever used for haulage in normal circumstances. Mk3 EMUs, other than 442s and 325s, have tightlock couplings which are incompatable with hauled stock couplings other than with an adapter or in emergencies. Like second generation DMUs they also have incompatable brakes. Modern EMUs are the same or have Dellner couplers.
