Celtic did not develop from the Urnfield complex, it predates Urnfield (according to recent linguistic publications). It seems that ethnogenesis and expansion of the Celts took place already in the Bronze Age (not during the Iron Age as thought previously). This is in line with ancieng DNA findings too.
One user on Polish history forum cited recent linguistic publications which push back the age of Celtic languages:
http://www.historycy.org/index.php?showtopic=152158&st=675&p=1749127&#entry1749127
^^^
"The first phase of Indo-Europeization of the Iberian Peninsula, represented by Lusitanian inscriptions, has to be dated back to the Early Bronze Age."
^^^
"Ancestors of Celtiberians, according to linguists, split from the rest of Celts
already before the emergence of the Western Group of Urnfield Culture."
And here something in English, "The Language of the Ancient Lusitanians":
https://www.academia.edu/9563554/The_Language_and_the_Religion_of_the_Ancient_Lusitanians
Recent research on the chronology of Celtic expansion:
"(...) Chapter 9 gives a short description of the problem of the western expansions of the Indo-European tribes. The chronology of the Celtic invasions into the Hispanic Peninsula is reviewed. The present author accepts the hypothesis that the migration) of the Proto-Lusitanian tribes preceded all the Celtic invasions. He suggests (after Jan G. P. Best’s earlier proposal) that the proto-Lusitanian tribes were representatives of the so called Beaker culture, dating to 2600-1900 BC. This archaeological culture is found intermittently across Western Europe, from Ireland east to Hungary, and from Denmark south to Sicily (see map 20). According to James P. Mallory, the Beaker culture “has often been associated with the Indo- Europeans since there are good reasons to derive it from the area of the earlier Corded Ware culture (The Netherlands / Rhineland region is probably the most widely accepted), which is frequently regarded as early Indo-European. [...] Beakers are also sometimes linked with the spread of the domestic horse (in Ireland and parts of Iberia, for example), solar symbolism, weaponry, and the introduction of early metallurgy - all seen as Indo-European traits”. The findings of the Beaker culture in ancient Lusitania are abundant, so the hypothesis seems to be correct. What is more, the distribution of the late phase of the Beaker culture in the Hispanic Peninsula agrees with the distribution of the Indo-European place-names ending with -briga 'hill, castle (in the hill), town, city’ (see map 22), whereas the Iberian culture called El Argar connects with the distribution of the non-Indo-European place names beginning with Ili-, Ilti-. It is possible to suggest that the proto-Lusitanian tribes originated from the Netherlands and the Rhineland region. There are many lexical and phonological similarities between the onomastics of the Gallia Belgica, which was inhabited by the Belgians (i.e. an unknown Indo-European nation located “zwischen Germanen und Kelten”) and that of the Lusitania. The Proto-Belgians and the Proto-Lusitanians had to represent two branches of a Pre-Celtic population of Indo-European origin. (...)"
In other words, Iberia and Britain could already be Celtic-speaking during the Bronze Age.
Hallstatt and La Tene were not Proto-Celtic cultures and were not ancestral to all of Celts.
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Celtiberians and Lepontic-speakers according to linguists split from the rest of Celts around the middle of the 2nd millennium BCE, during the disintegration of the Tumuli Cultures, and came to Iberia and Italy during the Middle Bronze Age.
Celts in Italy:
"Diffusion of Canegrate culture
The Canegrate culture was a civilization of Prehistoric Italy who developed from the recent Bronze Age (13th century BC) until the Iron Age, in the areas of what are now western Lombardy, eastern Piedmont, and Ticino. Canegrate represented a completely new cultural dynamic to the area expressed in pottery and bronzework making it a typical example of the western Hallstatt culture.
The name comes from the locality of Canegrate in Lombardy, south of Legnano and 25 km north of Milan, where Guido Sutermeister discovered important archaeological finds (approximately 50 tombs with ceramics and metallic objects). The site was first excavated in 1926 in the area of Rione Santa Colomba, and systematic excavation occurred between March 1953 and autumn 1956, which led to the discovery of a necropolis of 165 tomb. It is one of the richer archeological sites of Northern Italy.
The necropolis found in Canegrate is very similar to those realized in the same period in the north of Alps. It represents the first migratory wave of the proto-Celtic population from the northwest part of the Alps that, through the Alpine passes, had already penetrated and settled in the western Po valley between Lake Maggiore and Lake Como (Scamozzina culture). They brought a new funerary practice—cremation—which supplanted inhumation."
