Travellers -- indigenous hereditary itinerant groups -- are thought of as quintessentially Irish nowadays thanks to the filmcraft of Guy Ritchie. But some of these groups in the UK originate in various regions of Britain. On mainland Europe, one finds:
Were Traveller peoples once much more widespread, to the point of being ubiquitous, across Europe? Could one find, for example, present day people in Italy or Poland whose ancestors led a very similar lifestyle? I ask because such groups seem to have remained primarily in Europe's relative hinterlands, which makes me think they are a tiny remaining fragment of what was once a much more prevalent societal phenomenon. When did this phenomenon become less prevalent? That is to say, how far back in history would one have to go to find a time when a native Traveller population could be found in nearly every corner of Europe?
I realize this might not be the best sub for this question, since traditionally, from my understanding, Travellers keep no history and see themselves as having no need for history -- all is ephemeral for them except family ties -- and in turn, most European historians have returned the favor and written these peoples out of the historical record.
Also, what is the causal relationship between the presence of indigenous Traveller populations in Europe and the presence of Roma bands, who are not indigenous to Europe? Did Traveller peoples develop in imitation of the newly arrived Roma in the early middle ages? Or was it the other way -- did Roma find an economic niche in their new home in Europe by taking well trodden paths established by much older indigenous groups who lived a similar lifestyle?
Unfortunately, your question is probably fairly hard to answer for precisely the reasons you mention: modern-day Traveller groups tend not to have extensive written histories, and the origins stories told both by the Travellers and the people around them are often shrouded in folklore and conjecture.
This answer of mine from a year ago about Irish Travellers may help a bit if you're interested into the origins of that particular Travelling community:
While it won't necessarily make the issue clearer for you, I think one point is particularly salient:
Travellers have also traditionally held professions that would have been conducive to being on the road, prompting a "chicken-and-egg" kind of debate (did they take up those jobs because they were on the road, or did they go on the road because of their jobs?).
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The term "tinker," which describes the metalwork traditionally done by Travellers and has been used as both an endo- and exonym for the group, shows up as "tynker" or "tynkler" in the 12th century, although whether or not it was linked with a class of nomadic people is debated.
There have been trades that necessitate itinerancy for millenia. In Ireland, the people who took up some of those trades (especially tinworkers, travelling musicians, peddlers and animal traders) eventually formed a part of an ethnic group with a separate identity from the rest of the people on the island. Which one preceded the other is still up for debate, but for the most part, tinkers, peddlers, etc. in Ireland were almost entirely understood to be a part of the travelling community.
If someone were to dive into researching itinerant groups in Europe, I think that this thread would be the most productive. Whether or not people with traditionally itinerant jobs like tinkers, peddlers, et al. were considered "normal" people with a different profession, or were classed under a specific, common grouping would give you a sense of whether or not there was a concept of a cohesive travelling identity.
The one question of yours I can answer, at least in relation to Ireland, is
Also, what is the causal relationship between the presence of indigenous Traveller populations in Europe and the presence of Roma bands, who are not indigenous to Europe? Did Traveller peoples develop in imitation of the newly arrived Roma in the early middle ages?
The Roma did not have a very large presence in Ireland until relatively recently, and even now there are only a few thousand. So in the case of Irish Travellers, they developed mostly distinct from the Roma (I get to that a bit in my answer above).