No specific data from the UK.
However, there are different types of barges.
So called "Schute" is what I guess translates to tug barge.

These look roughly like a normal ship with a usual bow and stern.
These are always pulled.
So called "Leichter" (I guess it really translates to lighter) can be pushed and pulled but usually they are pushed.

There are some restrictions as not all kinds of lighter can be at the front, there always has to be some kind of Bow at the front, not all lighters have one.
Bow does not neccessarily mean it's peaky, often it's just a slope, which will allow multiple of such to be coubled and pushed as an up to 3x3 assembly (in Europe)
I could not find any exact data about how many can be pulled but only found images of single lighter barges being pulled.
Back to simutrans:
"unpowered tug barge" of any kind should not be pushed.
"steel hull unpowered barge" of any kind should be able to be assembled and pushed as a grid of up to 3x3. As this is not possible, I guess we should simply allow any number in a row to be pushed.
"diesel barge" of any kind (including the lightweight) should be able to pull exactly one steel unpowered barge. This would be possible if we copy each once for push and once for pull operation but I don't think we should do that and instead simply allow any number of pulled barges.